hassan gadain

King Saud University, Mathematics, Faculty Member

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King Saud University

Prirodno matematicki fakultet

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Papers by hassan gadain

Note on Relation between Double Laplace Transform and Double Differential Transform

Abstract and Applied Analysis, 2013

Double differential transform method has been employed to compute double Laplace transform. To il... more

$From the previous lemma, we know that, for m,n > 1, lim, 69 Dpal(r"/r!)\(-py)} = 0, and limg . Dey {(k"/ k!)(—sp)*} = 0, we have the following form:$

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A Note on Double Laplace Transform and Telegraphic Equations

Abstract and Applied Analysis, 2013

Double Laplace transform is applied to solve general linear telegraph and partial integrodifferen... more

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On some applications of a new integral transform

In this work a new integral transform, namely Sumudu transform was applied to solve linear ordina... more In this work a new integral transform, namely Sumudu transform was applied to solve linear ordinary differential equation with and without constant coefficients having convolution terms. In particular we apply Sumudu transform technique to solve Spring-Mass systems, Population Growth and financial problem.

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$Research paper thumbnail of Comparison of Sumudu and Laplace decomposition method for solving fractional Lane-Emden type differential equations$

Comparison of Sumudu and Laplace decomposition method for solving fractional Lane-Emden type differential equations

by hassan gadain and Eltayeb abdeldaim

Journal of Progressive Research in Mathematics, 2017

In this work we discuss the solution of delay differential equations of the fractional order of ... more

Nonlinear Singular One Dimensional Thermo-Elasticity Coupled System and Double Laplace Decomposition Methods

Filomat, 2016

In this work, combined double Laplace transform and Adomian decomposition method is presented to ... more In this work, combined double Laplace transform and Adomian decomposition method is presented to solve nonlinear singular one dimensional thermo-elasticity coupled system. Also we prove in this work the convergence of double Laplace transform decomposition method applied to our problem. By using one example, our proposed method is illustrated and the obtained results are confirmed.

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$Research paper thumbnail of Comparison of Sumudu and Laplace decomposition method for solving fractional Lane-Emden type differential equations$

Comparison of Sumudu and Laplace decomposition method for solving fractional Lane-Emden type differential equations

Journal of Progressive Research in Mathematics, 2017

In this work we discuss the solution of delay differential equations of the fractional order of ... more

Solving coupled pseudo-parabolic equation using a modified double Laplace decomposition method

Acta Mathematica Scientia

$Research paper thumbnail of A priori bounds of the solution of a one point IBVP for a singular fractional evolution equation$

A priori bounds of the solution of a one point IBVP for a singular fractional evolution equation

Advances in Difference Equations

A priori bounds constitute a crucial and powerful tool in the investigation of initial boundary v... more A priori bounds constitute a crucial and powerful tool in the investigation of initial boundary value problems for linear and nonlinear fractional and integer order differential equations in bounded domains. We present herein a collection of a priori estimates of the solution for an initial boundary value problem for a singular fractional evolution equation (generalized time-fractional wave equation) with mass absorption. The Riemann–Liouville derivative is employed. Results of uniqueness and dependence of the solution upon the data were obtained in two cases, the damped and the undamped case. The uniqueness and continuous dependence (stability of solution) of the solution follows from the obtained a priori estimates in fractional Sobolev spaces. These spaces give what are called weak solutions to our partial differential equations (they are based on the notion of the weak derivatives). The method of energy inequalities is used to obtain different a priori estimates.

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Application of double natural decomposition method for solving singular one dimensional Boussinesq equation

Filomat

In this work, a combined form of the double Natural transform method with the Adomian decompositi... more In this work, a combined form of the double Natural transform method with the Adomian decomposition method is developed for analytic treatment of the linear and nonlinear singular one dimensional Boussinesq equations. Two examples are provided to illustrate the simplicity and reliability of this method. Moreover, the results show that the proposed method is effective and is easy to implement for certain problems in science and engineering.

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Nonlinear singular one dimensional thermo-elasticity coupled system and double Laplace decomposition methods

Filomat

In this work, combined double Laplace transform and Adomian decomposition method is presented to ... more In this work, combined double Laplace transform and Adomian decomposition method is presented to solve nonlinear singular one dimensional thermo-elasticity coupled system. Moreover, the convergence proof of the double Laplace transform decomposition method applied to our problem. By using one example, our proposed method is illustrated and the obtained results are confirmed.

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On Some Initial and Initial Boundary Value Problems for Linear and Nonlinear Boussinesq Models

Symmetry

The main concern of this paper is to apply the modified double Laplace decomposition method to a ... more The main concern of this paper is to apply the modified double Laplace decomposition method to a singular generalized modified linear Boussinesq equation and to a singular nonlinear Boussinesq equation. An a priori estimate for the solution is also derived. Some examples are given to validate and illustrate the method.

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On a nonlinear singular one-dimensional parabolic equation and double Laplace decomposition method

Advances in Mechanical Engineering

In this article, the double Laplace transform and Adomian decomposition method are used to solve ... more In this article, the double Laplace transform and Adomian decomposition method are used to solve the nonlinear singular one-dimensional parabolic equation. In addition, we studied the convergence analysis of our problem. Using two examples, our proposed method is illustrated and the obtained results are confirmed.

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Application of double Laplace decomposition method for solving singular one dimensional system of hyperbolic equations

The Journal of Nonlinear Sciences and Applications

In this paper, the Adomain decomposition methods and double Laplace transform methods are combine... more In this paper, the Adomain decomposition methods and double Laplace transform methods are combined to study linear and nonlinear singular one dimensional system of hyperbolic equations. In addition, we check the convergence of double Laplace transform decomposition method applied to our problems. Furthermore, we illustrate our proposed methods by using some examples.

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Coupled singular and non singular thermoelastic system and Double Laplace Decomposition method

New Trends in Mathematical Science, 2016

In this paper, the double Laplace decomposition methods are applied to solve the non singular and... more

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A note on the comparison between laplace and sumudu transforms

In this paper, we discuss the existence of double Sumudu transform and study relationships betwee... more

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On Finite Product of Convolutions and Classifications of Hyperbolic and Elliptic Equations

In this paper we consider the linear second order partial differential equation with non-constant... more In this paper we consider the linear second order partial differential equation with non-constant coefficients; then by using the double convolution product we produce new equations with polynomials coefficients and we classify the new equations. It is shown that the classifications of hyperbolic and elliptic new equations are similar to the original equations that is the classification is invariant after finite double convolutions product.

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Research Article A Note on Wave Equation and Convolutions

We study the first-order nonhomogenous wave equation. We extend the convolution the- orem into a ... more

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On finite products of convolutions and classifications of hyperbolic and elliptic equations

Mathematical and Computer Modelling, 2011

In this paper we consider the linear second order partial differential equation with nonconstant ... more In this paper we consider the linear second order partial differential equation with nonconstant coefficients; then by using the double convolution product we produce new equations with polynomials coefficients and we classify the new equations. It is shown that the classifications of hyperbolic and elliptic new equations are similar to the original equations that is the classification is invariant after finite double convolutions product.

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An analysis on classifications of hyperbolic and elliptic PDEs

Mathematical Sciences, 2012

Purpose: Our aim in this study is to generate some partial differential equations (PDEs) with var... more Purpose: Our aim in this study is to generate some partial differential equations (PDEs) with variable coefficients by using the PDEs with non-constant coefficients. Methods: Then by applying the single and double convolution products, we produce some new equations having polynomials coefficients. We then classify the new equations on using the classification method for the second order linear partial differential equations. Results: Classification is invariant under single and double convolutions by applying some conditions, that is, we identify some conditions where a hyperbolic equation will be hyperbolic again after single and double convolutions. Conclusions: It is shown that the classifications of the new PDEs are related to the coefficients of polynomials which are considered during the process of convolution product.

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Some Remarks on the Sumudu and Laplace Transforms and Applications to Differential Equations

ISRN Applied Mathematics, 2012

We study the relationship between Sumudu and Laplace transforms and further make some comparison ... more We study the relationship between Sumudu and Laplace transforms and further make some comparison on the solutions. We provide some counterexamples where if the solution of differential equations exists by Laplace transform, the solution does not necessarily exist by using the Sumudu transform; however, the examples indicate that if the solution of differential equation by Sumudu transform exists then the solution necessarily exists by Laplace transform.

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Note on Relation between Double Laplace Transform and Double Differential Transform

Abstract and Applied Analysis, 2013

Double differential transform method has been employed to compute double Laplace transform. To il... more

$From the previous lemma, we know that, for m,n > 1, lim, 69 Dpal(r"/r!)\(-py)} = 0, and limg . Dey {(k"/ k!)(—sp)*} = 0, we have the following form:$

Download

A Note on Double Laplace Transform and Telegraphic Equations

Abstract and Applied Analysis, 2013

Double Laplace transform is applied to solve general linear telegraph and partial integrodifferen... more

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On some applications of a new integral transform

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$Research paper thumbnail of Comparison of Sumudu and Laplace decomposition method for solving fractional Lane-Emden type differential equations$

Comparison of Sumudu and Laplace decomposition method for solving fractional Lane-Emden type differential equations

by hassan gadain and Eltayeb abdeldaim

Journal of Progressive Research in Mathematics, 2017

In this work we discuss the solution of delay differential equations of the fractional order of ... more

Nonlinear Singular One Dimensional Thermo-Elasticity Coupled System and Double Laplace Decomposition Methods

Filomat, 2016

Download

$Research paper thumbnail of Comparison of Sumudu and Laplace decomposition method for solving fractional Lane-Emden type differential equations$

Comparison of Sumudu and Laplace decomposition method for solving fractional Lane-Emden type differential equations

Journal of Progressive Research in Mathematics, 2017

In this work we discuss the solution of delay differential equations of the fractional order of ... more

Solving coupled pseudo-parabolic equation using a modified double Laplace decomposition method

Acta Mathematica Scientia

$Research paper thumbnail of A priori bounds of the solution of a one point IBVP for a singular fractional evolution equation$

A priori bounds of the solution of a one point IBVP for a singular fractional evolution equation

Advances in Difference Equations

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Application of double natural decomposition method for solving singular one dimensional Boussinesq equation

Filomat

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Nonlinear singular one dimensional thermo-elasticity coupled system and double Laplace decomposition methods

Filomat

In this work, combined double Laplace transform and Adomian decomposition method is presented to ... more In this work, combined double Laplace transform and Adomian decomposition method is presented to solve nonlinear singular one dimensional thermo-elasticity coupled system. Moreover, the convergence proof of the double Laplace transform decomposition method applied to our problem. By using one example, our proposed method is illustrated and the obtained results are confirmed.