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Kacem Belghaba

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Universitat de València

National Institute of Technology, Calicut

Viacheslav Kuleshov

Stockholm University

Kamelia Spassova

Sofia University "St. Kliment Ohridski"

Universitat Politecnica de Catalunya

Semarang State University

University of Regensburg

Fatimah Khurniawanty

Hasanuddin University

Università di Sassari

Armando Marques-Guedes

UNL - New University of Lisbon

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Papers by Kacem Belghaba

$Research paper thumbnail of Compactons solutions for the fractional nonlinear dispersive K(2,2) equations by the homotopy perturbation method$

Compactons solutions for the fractional nonlinear dispersive K(2,2) equations by the homotopy perturbation method

Malaya journal of matematik, 2016

In this paper, the homotopy perturbation is successively used to obtain approximate analytical so... more In this paper, the homotopy perturbation is successively used to obtain approximate analytical solutions of the nonlinear dispersive K(2, 2) equation with time and space derivative. Comparison between the numerical and the exact solutions revealed that HPM is an alternative analytical method for solving fractional differential equations.

Approximate Solutions to Fractional Multi-Dimensional Navier-Stokes Equation Using the (FHPTM)

DergiPark (Istanbul University), Apr 25, 2022

This work focuses on presenting a reliable method, called fractional homotopy perturbation transf... more This work focuses on presenting a reliable method, called fractional homotopy perturbation transform method (FHPTM) to solve nonlinear Naviers Stoks equations with the Caputo type fractional derivatives. The (FHPTM) is a combination of Laplace transform and homotopy perturbation method (He-Laplace method). He's polynomial is used to simplify the nonlinearity which arise in our considered equation. Furthermore, three numerical examples are presented, it is supported by graphs and tables to compare solutions with little computational effort, which confirms the effectiveness and accuracy of the current method.

Fractional Variational Iteration Method and Adomian’s Decomposition Method: Applications to Fractional Burgers Kuramoto KdV Equation via Hadamard Derivative

Communications in Mathematics and Applications, Jun 30, 2021

This paper presents the analytical solutions of the Fractional Burgers Kuramoto KdV equation by t... more This paper presents the analytical solutions of the Fractional Burgers Kuramoto KdV equation by the variational iteration method and Adomian’s decomposition method using Hadamard fractional derivative. By using initial conditions, the explicit solutions of the Burgers Kuramoto Kdv equation have been presented. The fractional derivatives are considered according to the Hadamard’s approach. Two examples are given for illustrate to implement variational iteration method and Adomian’s decomposition method for fractional Burgers Kuramoto KdV equation.

Numerical Solution for Solving Fractional Differential Equations using Shifted Chebyshev Wavelet

General Letters in Mathematics, 2017

In this paper, we are interested to develop a numerical method based on the Chebyshev wavelets fo... more In this paper, we are interested to develop a numerical method based on the Chebyshev wavelets for solving fractional order differential equations (FDEs). As a result of the presentation of Chebyshev wavelets, we highlight the operational matrix of the fractional order derivative through wavelet-polynomial matrix transformation which was utilized together with spectral and collocation methods to reduce the linear FDEs, to a system of algebraic equations. This method is a more simple technique of obtaining the operational matrix with straight forward applicability to the FDEs. The main characteristic behind the approach using this technique is that only a small number of shifted Chebyshev polynomials is needed to obtain a satisfactory results. Illustrative examples reveal that the present method is very effective and convenient for linear FDEs.

Homotopy Perturbation Method for Solving the Fractional Fisher's Equation

International Journal of Analysis and Applications, Jan 17, 2016

In this paper, we apply the modified HPM suggested by Momani and al. [23] for solving the time-fr... more In this paper, we apply the modified HPM suggested by Momani and al. [23] for solving the time-fractional Fisher's equation and we use the classical HPM to derive numerical solutions of the space-fractional Fisher's equation. We compared our solution with the exact solution. The results show that the HPM modified is an appropriate method for solving nonlinear fractional derivative equations.

Investigation of Conformable Double Shehu Transform for Solving Some Fractional Differential Partial Equations

Journal of Science and Arts

In this paper, we generalize the concept of single conformable Sehu transformation (CSHT) to doub... more In this paper, we generalize the concept of single conformable Sehu transformation (CSHT) to double conformable transformation (CDFSHT). Moreover, we are able to prove some theorems and properties related to this work. We apply the double conformable Sehu transform to solve the initial and boundary problems of linear and (non)homogenous conformable fractional partial differential equations (PDEs). The validity and the applicability of the proposed technique are shown by three numerical examples. Mathematica software is used for Euclidean division of polynomials and drawing graphs.

Shehu Variational Iteration Method For Solve Some Fractional Differential Equations

Communications in Mathematics and Applications

$Research paper thumbnail of Anti-periodic boundary value problems for Caputo-Fabrizio fractional impulsive differential equations$

Anti-periodic boundary value problems for Caputo-Fabrizio fractional impulsive differential equations

Mathematica Moravica

In this paper, we shall discuss the existence and uniqueness of solutions for a nonlinear anti-pe... more In this paper, we shall discuss the existence and uniqueness of solutions for a nonlinear anti-periodic boundary value problem for fractional impulsive differential equations involving a Caputo-Fabrizio fractional derivative of order r ∈ (0, 1). Our results are based on some fixed point theorem, nonlinear alternative of Leray-Schauder type and coupled lower and upper solutions.

Analytical Study of Fractional Reaction-Diffusion Brusselator System

Istanbul University - DergiPark, Jun 26, 2022

In this paper, a time fractional reaction-diffusion Brusselator system with the Caputo type fract... more In this paper, a time fractional reaction-diffusion Brusselator system with the Caputo type fractional derivatives, is solved by Laplace Adomian decomposition method (LADM). Two numerical examples supported by graphics, tables, and discussion are provided, by comparing the numerical results obtained with the exact solution when α = β = 1, it is observed that they are in perfect agreement, this confirms the accuracy and smoothness of the current method.

Shehu Conformable Fractional Transform, Theories and Applications

Çankaya University Journal of Humanities and Social Sciences, May 1, 2021

The Analytical Solution of Telegraph Equation of Space-Fractional Order Derivative by the Aboodh Transform Method

International Journal of Analysis and Applications, 2020

In this article, an analytical solution based on the series expansion method is proposed to solve... more In this article, an analytical solution based on the series expansion method is proposed to solve the telegraph equation of space-fractional order (TESFO), namely the Aboodh transformation method (ATM) subjected to the appropriate initial condition. Using ATM, it is possible to find exact solution or a closed approximate solution of a differential equation. Finally, several numerical examples are given to illustrate the accuracy and stability of this method.

$Research paper thumbnail of Adomian decomposition method for solving fractional nonlinear differential equations$

Adomian decomposition method for solving fractional nonlinear differential equations

Applied Mathematics and Computation, 2006

In this article, we have discussed a new application of Adomian decomposition method on time frac... more In this article, we have discussed a new application of Adomian decomposition method on time fractional nonlinear fractional differential equations. Three models with fractional-time derivative of order a, 0 < a < 1 are considered and solved by means of Adomian decomposition method. The behaviour of Adomian solutions and the effects of different values of a are investigated. Numerical examples are tested to illustrate the pertinent feature of the proposed algorithm.

$Fig. la. Numerical solution of the generalized fractional time-KdV equation with a fixed values p = 6, K=0.1, A=0.2 and « = 1/2. where c is a constant. As shown in Figs. 2a and 2b the comparison shows that the two solutions are equivalent.$

$Fig. 1b. Numerical solution of the generalized fractional time-KdV equation with a fixed values p = 8, K=0.1, A = 0.2 and « = 3/4.$

$Fig. 2a. Numerical solution of the generalized fractional time-KdV equation with a fixed values p= 4, K=0.1, A=0.2 anda=1.$

$Fig. 2b. Exact solution of the generalized fractional time-KdV equation (20) with a fixed values p= 4, K=0.1 and A =0.2 It is worth noting that the accuracy of the Adomian approach is significantly enhanced by calculation as 1any more terms as we like. This may be made but only at the expense of a considerable increase in the com- lexity of analysis.$

$Fig. 3a. Numerical solution for the generalized fractional Burgers—Fisher equation with a fixed values r= 4, p=0.1, g = —0.0025 anc a = 1/2.$

$Fig. 3b. Numerical solution for the generalized fractional time-Burgers—Fisher equation with a fixed values r= 4, p = 0.1, ¢g = —0.0025 and a = 3/4.$

$Fig. 3d. Numerical solution for the generalized fractional Burgers—Fisher equation with a fixed values r= 2, p=0.1, g = —0.0025 ar a=1.$

$Fig. 4a. The numerical solution of u(x,t) by Adomian decomposition method with a fractional order « = 3/4 and k = 1.$

$Fig. 4b. The numerical solution of u(x,t) by Adomian decomposition method with a fractional order « = 1/2 and k= 1.$

$Fig. 4c. The numerical solution of v(x,7) by Adomian decomposition method with a fractional order « = 3/4 and k = 1.$

$Fig. 4d. The numerical solution of u(x,t) by Adomian decomposition method with a fractional order « = 1/2 and k=1.$

$Fig. 5b. The numerical solution of u(x,t) by Adomian decomposition method with a fractional order « = 1.$

$Fig. 5d. The numerical solution of u(x,t) by Adomian decomposition method with a fractional order « = 1.$

He’s Variational Iteration Method for Solving Multi-Dimensional of Navier Stokes Equation

International Journal of Analysis and Applications, 2020

In this paper, He's variational iteration method (VIM), established by He in (1999), is adopted t... more In this paper, He's variational iteration method (VIM), established by He in (1999), is adopted to solve two and three dimensional of Navier-Stokes equation in cartesian coordinates. This method is a powerful tool to handle linear and nonlinear models. The main property of the method is its softness and ability to solve nonlinear equations, accurately and easily. Using variational iteration method, it is possible to find the exact solution or a closed approximate solution of a problem. To illustrate the capacity and reliability of this method, some examples and numerical results are provided.

Solving $$(1+n)$$-Dimensional Fractional Burgers Equation by Natural Decomposition Method

Numerical Analysis and Applications

ABSTRACT In this paper, we combine the natural transform with the Adomian decomposition for solvi... more ABSTRACT In this paper, we combine the natural transform with the Adomian decomposition for solving nonlinear partial differential equations with time-fractional derivatives. We apply this method to obtain approximate analytical solutions of $$(1+n)$$ ( 1 + n ) -dimensional fractional Burgers equations. Some illustrative examples are given, which show this to be a very efficient and accurate analytical method for solving nonlinear fractional partial differential equations.

$Research paper thumbnail of Fractional natural decomposition method for solving fractional system of nonlinear equations of unsteady flow of a polytropic gas$

Fractional natural decomposition method for solving fractional system of nonlinear equations of unsteady flow of a polytropic gas

Nonlinear Studies, 2018

In this paper, we apply the fractional natural decomposition method suggested by M. S. Rawashdeh ... more In this paper, we apply the fractional natural decomposition method suggested by M. S. Rawashdeh et al. in [20] to derive approximate analytical solutions to system of nonlinear equations of unsteady flow of a polytropic gas with time-fractional derivatives. The proposed method (FNDM) has been applied successfully to solve this system. So, the results re-confirm that this method is very efficient and accurate to solve others nonlinear systems problems.

$Research paper thumbnail of An accurate method for nonlinear local fractional Wave-Like equations with variable coefficients$

An accurate method for nonlinear local fractional Wave-Like equations with variable coefficients

Computational Methods for Differential Equations, 2020

The basic motivation of the present study is to apply the local fractional Sumudu variational ite... more The basic motivation of the present study is to apply the local fractional Sumudu variational iteration method (LFSVIM) for solving nonlinear wave-like equations with variable coefficients and within local fractional derivative. The derivatives operators are taken in the local fractional sense. The results show that the LFSVIM is an appropriate method to find non-differentiable solutions for similar problems. The results of the solved examples showed the flexibility of applying this method and its ability to reach accurate results even with these new differential equations.

Fractional higher dimensional initial boundary value problems via variational iteration method coupled with Elzaki transform

The basic motivation of the present study is to extend the application of variational iteration m... more The basic motivation of the present study is to extend the application of variational iteration method (VIM) and Elzaki transform method for solving linear and nonlinear higher dimensional initial boundary value problems with time-fractional derivatives. The proposed algorithm provides the solution in a rapid convergent series which may lead to the solution in a closed form.

$Research paper thumbnail of Local fractional Sumudu decomposition method for linear partial differential equations with local fractional derivative$

Local fractional Sumudu decomposition method for linear partial differential equations with local fractional derivative

Journal of King Saud University - Science, 2017

In the paper, a combined form of the Sumudu transform method with the Adomian decomposition metho... more In the paper, a combined form of the Sumudu transform method with the Adomian decomposition method in the sense of local fractional derivative, is proposed to solve fractional partial differential equations. This method is called the local fractional Sumudu decomposition method (LFSDM) and is used to describe the non-differentiable problems. It would be interesting to apply LFSDM to some well-known problems to see the benefits obtained.

Solution of Newel-Whitehead-Segel Equation Using Conformable Fractional Sumudu Decomposition Method

Journal of Science and Arts

In the present paper, a numerical method is proposed to solve the time fractional Newel-Whitead-S... more In the present paper, a numerical method is proposed to solve the time fractional Newel-Whitead-Segel equation subject to initial condition. This method is based d on the unification of conformable Sumudu transform (CST) and Adomian decomposition method (ADM), and then it is used to find the analytical solutions of linear-nonlinear fractional PDE’s. The test examples are given for illustration

Homotopy Perturbation Method Combined with ZZ Transform to Solve Some Nonlinear Fractional Differential Equations

International Journal of Analysis and Applications, 2019

The idea proposed in this work is to extend the ZZ transform method to resolve the nonlinear frac... more The idea proposed in this work is to extend the ZZ transform method to resolve the nonlinear fractional partial differential equations by combining them with the so-called homotopy perturbation method (HPM). We apply this technique to solve some nonlinear fractional equations as: nonlinear time-fractional Fokker-Planck equation, the cubic nonlinear time-fractional Schrödinger equation and the nonlinear timefractional KdV equation. The fractional derivative is described in the Caputo sense. The results show that this is the appropriate method to solve somme models of nonlinear partial differential equations with time-fractional derivative.

$Research paper thumbnail of Compactons solutions for the fractional nonlinear dispersive K(2,2) equations by the homotopy perturbation method$

Compactons solutions for the fractional nonlinear dispersive K(2,2) equations by the homotopy perturbation method

Malaya journal of matematik, 2016

In this paper, the homotopy perturbation is successively used to obtain approximate analytical so... more In this paper, the homotopy perturbation is successively used to obtain approximate analytical solutions of the nonlinear dispersive K(2, 2) equation with time and space derivative. Comparison between the numerical and the exact solutions revealed that HPM is an alternative analytical method for solving fractional differential equations.

Approximate Solutions to Fractional Multi-Dimensional Navier-Stokes Equation Using the (FHPTM)

DergiPark (Istanbul University), Apr 25, 2022

This work focuses on presenting a reliable method, called fractional homotopy perturbation transf... more This work focuses on presenting a reliable method, called fractional homotopy perturbation transform method (FHPTM) to solve nonlinear Naviers Stoks equations with the Caputo type fractional derivatives. The (FHPTM) is a combination of Laplace transform and homotopy perturbation method (He-Laplace method). He's polynomial is used to simplify the nonlinearity which arise in our considered equation. Furthermore, three numerical examples are presented, it is supported by graphs and tables to compare solutions with little computational effort, which confirms the effectiveness and accuracy of the current method.

Fractional Variational Iteration Method and Adomian’s Decomposition Method: Applications to Fractional Burgers Kuramoto KdV Equation via Hadamard Derivative

Communications in Mathematics and Applications, Jun 30, 2021

This paper presents the analytical solutions of the Fractional Burgers Kuramoto KdV equation by t... more This paper presents the analytical solutions of the Fractional Burgers Kuramoto KdV equation by the variational iteration method and Adomian’s decomposition method using Hadamard fractional derivative. By using initial conditions, the explicit solutions of the Burgers Kuramoto Kdv equation have been presented. The fractional derivatives are considered according to the Hadamard’s approach. Two examples are given for illustrate to implement variational iteration method and Adomian’s decomposition method for fractional Burgers Kuramoto KdV equation.

Numerical Solution for Solving Fractional Differential Equations using Shifted Chebyshev Wavelet

General Letters in Mathematics, 2017

In this paper, we are interested to develop a numerical method based on the Chebyshev wavelets fo... more In this paper, we are interested to develop a numerical method based on the Chebyshev wavelets for solving fractional order differential equations (FDEs). As a result of the presentation of Chebyshev wavelets, we highlight the operational matrix of the fractional order derivative through wavelet-polynomial matrix transformation which was utilized together with spectral and collocation methods to reduce the linear FDEs, to a system of algebraic equations. This method is a more simple technique of obtaining the operational matrix with straight forward applicability to the FDEs. The main characteristic behind the approach using this technique is that only a small number of shifted Chebyshev polynomials is needed to obtain a satisfactory results. Illustrative examples reveal that the present method is very effective and convenient for linear FDEs.

Homotopy Perturbation Method for Solving the Fractional Fisher's Equation

International Journal of Analysis and Applications, Jan 17, 2016

In this paper, we apply the modified HPM suggested by Momani and al. [23] for solving the time-fr... more In this paper, we apply the modified HPM suggested by Momani and al. [23] for solving the time-fractional Fisher's equation and we use the classical HPM to derive numerical solutions of the space-fractional Fisher's equation. We compared our solution with the exact solution. The results show that the HPM modified is an appropriate method for solving nonlinear fractional derivative equations.

Investigation of Conformable Double Shehu Transform for Solving Some Fractional Differential Partial Equations

Journal of Science and Arts

In this paper, we generalize the concept of single conformable Sehu transformation (CSHT) to doub... more In this paper, we generalize the concept of single conformable Sehu transformation (CSHT) to double conformable transformation (CDFSHT). Moreover, we are able to prove some theorems and properties related to this work. We apply the double conformable Sehu transform to solve the initial and boundary problems of linear and (non)homogenous conformable fractional partial differential equations (PDEs). The validity and the applicability of the proposed technique are shown by three numerical examples. Mathematica software is used for Euclidean division of polynomials and drawing graphs.

Shehu Variational Iteration Method For Solve Some Fractional Differential Equations

Communications in Mathematics and Applications

$Research paper thumbnail of Anti-periodic boundary value problems for Caputo-Fabrizio fractional impulsive differential equations$

Anti-periodic boundary value problems for Caputo-Fabrizio fractional impulsive differential equations

Mathematica Moravica

In this paper, we shall discuss the existence and uniqueness of solutions for a nonlinear anti-pe... more In this paper, we shall discuss the existence and uniqueness of solutions for a nonlinear anti-periodic boundary value problem for fractional impulsive differential equations involving a Caputo-Fabrizio fractional derivative of order r ∈ (0, 1). Our results are based on some fixed point theorem, nonlinear alternative of Leray-Schauder type and coupled lower and upper solutions.

Analytical Study of Fractional Reaction-Diffusion Brusselator System

Istanbul University - DergiPark, Jun 26, 2022

In this paper, a time fractional reaction-diffusion Brusselator system with the Caputo type fract... more In this paper, a time fractional reaction-diffusion Brusselator system with the Caputo type fractional derivatives, is solved by Laplace Adomian decomposition method (LADM). Two numerical examples supported by graphics, tables, and discussion are provided, by comparing the numerical results obtained with the exact solution when α = β = 1, it is observed that they are in perfect agreement, this confirms the accuracy and smoothness of the current method.

Shehu Conformable Fractional Transform, Theories and Applications

Çankaya University Journal of Humanities and Social Sciences, May 1, 2021

The Analytical Solution of Telegraph Equation of Space-Fractional Order Derivative by the Aboodh Transform Method

International Journal of Analysis and Applications, 2020

In this article, an analytical solution based on the series expansion method is proposed to solve... more In this article, an analytical solution based on the series expansion method is proposed to solve the telegraph equation of space-fractional order (TESFO), namely the Aboodh transformation method (ATM) subjected to the appropriate initial condition. Using ATM, it is possible to find exact solution or a closed approximate solution of a differential equation. Finally, several numerical examples are given to illustrate the accuracy and stability of this method.

$Research paper thumbnail of Adomian decomposition method for solving fractional nonlinear differential equations$

Adomian decomposition method for solving fractional nonlinear differential equations

Applied Mathematics and Computation, 2006

In this article, we have discussed a new application of Adomian decomposition method on time frac... more In this article, we have discussed a new application of Adomian decomposition method on time fractional nonlinear fractional differential equations. Three models with fractional-time derivative of order a, 0 < a < 1 are considered and solved by means of Adomian decomposition method. The behaviour of Adomian solutions and the effects of different values of a are investigated. Numerical examples are tested to illustrate the pertinent feature of the proposed algorithm.

$Fig. la. Numerical solution of the generalized fractional time-KdV equation with a fixed values p = 6, K=0.1, A=0.2 and « = 1/2. where c is a constant. As shown in Figs. 2a and 2b the comparison shows that the two solutions are equivalent.$

$Fig. 1b. Numerical solution of the generalized fractional time-KdV equation with a fixed values p = 8, K=0.1, A = 0.2 and « = 3/4.$

$Fig. 2a. Numerical solution of the generalized fractional time-KdV equation with a fixed values p= 4, K=0.1, A=0.2 anda=1.$

$Fig. 2b. Exact solution of the generalized fractional time-KdV equation (20) with a fixed values p= 4, K=0.1 and A =0.2 It is worth noting that the accuracy of the Adomian approach is significantly enhanced by calculation as 1any more terms as we like. This may be made but only at the expense of a considerable increase in the com- lexity of analysis.$

$Fig. 3a. Numerical solution for the generalized fractional Burgers—Fisher equation with a fixed values r= 4, p=0.1, g = —0.0025 anc a = 1/2.$

$Fig. 3b. Numerical solution for the generalized fractional time-Burgers—Fisher equation with a fixed values r= 4, p = 0.1, ¢g = —0.0025 and a = 3/4.$

$Fig. 3d. Numerical solution for the generalized fractional Burgers—Fisher equation with a fixed values r= 2, p=0.1, g = —0.0025 ar a=1.$

$Fig. 4a. The numerical solution of u(x,t) by Adomian decomposition method with a fractional order « = 3/4 and k = 1.$

$Fig. 4b. The numerical solution of u(x,t) by Adomian decomposition method with a fractional order « = 1/2 and k= 1.$

$Fig. 4c. The numerical solution of v(x,7) by Adomian decomposition method with a fractional order « = 3/4 and k = 1.$

$Fig. 4d. The numerical solution of u(x,t) by Adomian decomposition method with a fractional order « = 1/2 and k=1.$

$Fig. 5b. The numerical solution of u(x,t) by Adomian decomposition method with a fractional order « = 1.$

$Fig. 5d. The numerical solution of u(x,t) by Adomian decomposition method with a fractional order « = 1.$

He’s Variational Iteration Method for Solving Multi-Dimensional of Navier Stokes Equation

International Journal of Analysis and Applications, 2020

In this paper, He's variational iteration method (VIM), established by He in (1999), is adopted t... more In this paper, He's variational iteration method (VIM), established by He in (1999), is adopted to solve two and three dimensional of Navier-Stokes equation in cartesian coordinates. This method is a powerful tool to handle linear and nonlinear models. The main property of the method is its softness and ability to solve nonlinear equations, accurately and easily. Using variational iteration method, it is possible to find the exact solution or a closed approximate solution of a problem. To illustrate the capacity and reliability of this method, some examples and numerical results are provided.

Solving $$(1+n)$$-Dimensional Fractional Burgers Equation by Natural Decomposition Method

Numerical Analysis and Applications

ABSTRACT In this paper, we combine the natural transform with the Adomian decomposition for solvi... more ABSTRACT In this paper, we combine the natural transform with the Adomian decomposition for solving nonlinear partial differential equations with time-fractional derivatives. We apply this method to obtain approximate analytical solutions of $$(1+n)$$ ( 1 + n ) -dimensional fractional Burgers equations. Some illustrative examples are given, which show this to be a very efficient and accurate analytical method for solving nonlinear fractional partial differential equations.

$Research paper thumbnail of Fractional natural decomposition method for solving fractional system of nonlinear equations of unsteady flow of a polytropic gas$

Fractional natural decomposition method for solving fractional system of nonlinear equations of unsteady flow of a polytropic gas

Nonlinear Studies, 2018

In this paper, we apply the fractional natural decomposition method suggested by M. S. Rawashdeh ... more In this paper, we apply the fractional natural decomposition method suggested by M. S. Rawashdeh et al. in [20] to derive approximate analytical solutions to system of nonlinear equations of unsteady flow of a polytropic gas with time-fractional derivatives. The proposed method (FNDM) has been applied successfully to solve this system. So, the results re-confirm that this method is very efficient and accurate to solve others nonlinear systems problems.

$Research paper thumbnail of An accurate method for nonlinear local fractional Wave-Like equations with variable coefficients$

An accurate method for nonlinear local fractional Wave-Like equations with variable coefficients

Computational Methods for Differential Equations, 2020

The basic motivation of the present study is to apply the local fractional Sumudu variational ite... more The basic motivation of the present study is to apply the local fractional Sumudu variational iteration method (LFSVIM) for solving nonlinear wave-like equations with variable coefficients and within local fractional derivative. The derivatives operators are taken in the local fractional sense. The results show that the LFSVIM is an appropriate method to find non-differentiable solutions for similar problems. The results of the solved examples showed the flexibility of applying this method and its ability to reach accurate results even with these new differential equations.

Fractional higher dimensional initial boundary value problems via variational iteration method coupled with Elzaki transform

The basic motivation of the present study is to extend the application of variational iteration m... more The basic motivation of the present study is to extend the application of variational iteration method (VIM) and Elzaki transform method for solving linear and nonlinear higher dimensional initial boundary value problems with time-fractional derivatives. The proposed algorithm provides the solution in a rapid convergent series which may lead to the solution in a closed form.

$Research paper thumbnail of Local fractional Sumudu decomposition method for linear partial differential equations with local fractional derivative$

Local fractional Sumudu decomposition method for linear partial differential equations with local fractional derivative

Journal of King Saud University - Science, 2017

In the paper, a combined form of the Sumudu transform method with the Adomian decomposition metho... more In the paper, a combined form of the Sumudu transform method with the Adomian decomposition method in the sense of local fractional derivative, is proposed to solve fractional partial differential equations. This method is called the local fractional Sumudu decomposition method (LFSDM) and is used to describe the non-differentiable problems. It would be interesting to apply LFSDM to some well-known problems to see the benefits obtained.

Solution of Newel-Whitehead-Segel Equation Using Conformable Fractional Sumudu Decomposition Method

Journal of Science and Arts

In the present paper, a numerical method is proposed to solve the time fractional Newel-Whitead-S... more In the present paper, a numerical method is proposed to solve the time fractional Newel-Whitead-Segel equation subject to initial condition. This method is based d on the unification of conformable Sumudu transform (CST) and Adomian decomposition method (ADM), and then it is used to find the analytical solutions of linear-nonlinear fractional PDE’s. The test examples are given for illustration

Homotopy Perturbation Method Combined with ZZ Transform to Solve Some Nonlinear Fractional Differential Equations

International Journal of Analysis and Applications, 2019

The idea proposed in this work is to extend the ZZ transform method to resolve the nonlinear frac... more The idea proposed in this work is to extend the ZZ transform method to resolve the nonlinear fractional partial differential equations by combining them with the so-called homotopy perturbation method (HPM). We apply this technique to solve some nonlinear fractional equations as: nonlinear time-fractional Fokker-Planck equation, the cubic nonlinear time-fractional Schrödinger equation and the nonlinear timefractional KdV equation. The fractional derivative is described in the Caputo sense. The results show that this is the appropriate method to solve somme models of nonlinear partial differential equations with time-fractional derivative.