I have Ph.D. Degree at 2009, Head of Mathematics Department since 2007, I interest Numerical analysis, Spline Interpolation function, Address: Sulaimani, Iraq
Interpolation by various types of splines is the standard procedure in many applications. In this... more Interpolation by various types of splines is the standard procedure in many applications. In this paper shall discuss the function, two and fourth derivatives of spline interpolation as an alternative to polynomial spline interpolation at the all intervals. The method is appropriate and solving of initial and boundary value problems, the results revealing that method is very effective and accurate.
The aim of this paper is to investigate the performance of the ninth degree spline method for sol... more The aim of this paper is to investigate the performance of the ninth degree spline method for solving the system of ordinary differential equations and to estimate the numerical solution in the whole interval. By considering the maximum absolute errors in the solution at grid points for different choices of step size, we conclude that ninth spline produces the accurate results in comparison with other methods. AMS Subject Classification Code: 41A25, 65H10, 47E05.
Fractional Polynomial Spline for Solving Differential Equations of Fractional Order
In this paper, we implement new approximate techniques, the fractional lacunary interpolation by ... more In this paper, we implement new approximate techniques, the fractional lacunary interpolation by spline function for s lving differential equations of fractional order. Convergence a nalysis, existence and uniqueness are shown by several theo rems in the classes of C3 andC4 depend on the degree of spline polynomials. The numerical re sults demonstrates the errors bounds is quite validity and applicability of this method.
Computational Method for Fractional Differential Equations Using Nonpolynomial Fractional Spline
Mathematical Sciences Letters, 2016
In this paper, a new fractional spline method of non-polynomial form have been considered to solv... more In this paper, a new fractional spline method of non-polynomial form have been considered to solve special linear fractional boundary-value problems. Using this fractional spline function a few consistency relations are derived for computing approximations to the solution of the problem. Convergence analysis and error estimates of this methods are discussed. Numerical results are provided to demonstrate the superiority of our methods.
The discrete delta Caputo-Fabrizio fractional differences and sums are proposed to distinguish th... more The discrete delta Caputo-Fabrizio fractional differences and sums are proposed to distinguish their monotonicity analysis from the sense of Riemann and Caputo operators on the time scale Z. Moreover, the action of Q− operator and discrete delta Laplace transform method are also reported. Furthermore, a relationship between the discrete delta Caputo-Fabrizio-Caputo and Caputo-Fabrizio-Riemann fractional differences is also studied in detail. To better understand the dynamic behavior of the obtained monotonicity results, the fractional difference mean value theorem is derived. The idea used in this article is readily applicable to obtain monotonicity analysis of other discrete fractional operators in discrete fractional calculus.
AL-Rafidain Journal of Computer Sciences and Mathematics
The mechanism of thin liquid films on solid surfaces is fundamental to a wide variety of phenomen... more The mechanism of thin liquid films on solid surfaces is fundamental to a wide variety of phenomena such as surface coatings in paint. A mathematical model is constructed to describe the two dimensions of steady thin liquid films flow on an inclined plane with the use of lubrication approximation, we have applied Navier-Stokes equations in two dimensional coordinates for flow of incompressible fluid with the specified boundary conditions, and the solution of the film thickness equation has been drawn for flow for several inclination angles which modify the shape of the emerging patterns and also we derived the third order differential
In this paper, we construct numerical algorithms for solving Magnetohidrodynamics(MHD) free conve... more In this paper, we construct numerical algorithms for solving Magnetohidrodynamics(MHD) free convection flow rate whichhas been discussed in detail. It is observed that, for a nonlinear system of differential equation, the spline model of ninedegree is used, effectiveness and accuracy of this new method are presented. Several theorems relating the order of theninth spline to the saturation of the estimator are proved. Some results of consistency are given and an applicationMHD system is given.
In the paper a mathematical model is developed by using numerical solution to study the non stati... more In the paper a mathematical model is developed by using numerical solution to study the non stationary heat equation in one dimension. This model leads to incorporate a cooling system for a computer radiator. The result of the model is compared with the stationary heat transfer model. The simulation results show the performance of non stationary model in terms of variation of temperature.
Composition Fractional Integral Inequality for the Reiman-Liouville type with applications
Journal of Zankoy Sulaimani - Part A
In this work, some integral inequalities of fractional order of Riemann-Liouville type are establ... more In this work, some integral inequalities of fractional order of Riemann-Liouville type are established, which generalized some know inequalities for [8]. These can be used in the analysis of various problems in the theory of certain classes of fractional differential equations and fractional integral equations. Also, some applications for the fractional differential and integral equations are also indicated. Fractional integral inequalities, Holder's inequality
In this paper, consisted in finding the nonpolynomial spline function and generalized it by fract... more In this paper, consisted in finding the nonpolynomial spline function and generalized it by fractional order. Other propose of this function was interpolating spline fractional derivatives, with their effective applications to numerically solving fractional boundary value problems. We also discussed the rate of convergence of the method with fractional order. The error bounds and convergence of our difference schemes for nonpolynomial spline with fractional order are theoretically established, this is done by computer program with the aid of the Maptlab 13 for all the above prescribed methods, and the numerical results for boundary value problems are also presented.
International Journal of Open Problems in Computer Science and Mathematics, 2015
In this paper, a new fractional spline function of polynomial form with the idea of the lacunary ... more In this paper, a new fractional spline function of polynomial form with the idea of the lacunary interpolation is considered to find approximate solution for fractional differential equations (FDEs). The proposed method is applicable for α ∈ (0, 1], where α denotes the order of the fractional derivative in the Caputo sense. Convergence analysis of the method is considered. Some illustrative examples are presented and the obtained results reveal that the proposed technique is very effective, convenient and quite accurate to such considered problems. The study is conducted through illustrative examples and error analysis.
In this paper, a quintic spline interpolation algorithm presented for the solution of second orde... more In this paper, a quintic spline interpolation algorithm presented for the solution of second order initial value problems with a new class of the lacunary spline interpolation based on quintic C4-splines as an approximation to the exact solution of such problems. Convergence analysis of the presented spline function was discussed, stability analysis has been carried out and two examples were considered for the numerical illustration of the presented technique. The results show that the presented quintic spline function which interpolates the lacunary data was efficient and effective for solving such problems.
Abstract This paper presents a formulation and a study of three interpolatory fractional splines ... more Abstract This paper presents a formulation and a study of three interpolatory fractional splines these are in the class of ma, m = 2, 4, 6, a = 0.5. We extend fractional splines function with uniform knots to approximate the solution of fractional equations. The developed of spline method is to analysis convergence fractional order derivatives and estimating error bounds. We propose spline fractional method to solve fractional differentiation equations. Numerical example is given to illustrate the applicability and accuracy of the methods.
Numerical Approximation of Fractional Differential Equations with Fractional Spline Function. Journal of Zankoy Sulaimani – Part A (JZS-A), and it will be published in Vol.(17), No.(3), (2015)
In this paper, we consider a new suitable lacunary fractional interpolation with the idea of the ... more In this paper, we consider a new suitable lacunary fractional interpolation with the idea of the spline function of polynomial form, and the method applied to solve linear fractional differential equations. The results obtained are in good agreement with the exact analytical solutions and the numerical results presented by several examples, results also show that the technique introduced here is robust and easy to apply.
Interpolation by various types of splines is the standard procedure in many applications. In this... more Interpolation by various types of splines is the standard procedure in many applications. In this paper shall discuss the function, two and fourth derivatives of spline interpolation as an alternative to polynomial spline interpolation at the all intervals. The method is appropriate and solving of initial and boundary value problems, the results revealing that method is very effective and accurate.
The aim of this paper is to investigate the performance of the ninth degree spline method for sol... more The aim of this paper is to investigate the performance of the ninth degree spline method for solving the system of ordinary differential equations and to estimate the numerical solution in the whole interval. By considering the maximum absolute errors in the solution at grid points for different choices of step size, we conclude that ninth spline produces the accurate results in comparison with other methods. AMS Subject Classification Code: 41A25, 65H10, 47E05.
Fractional Polynomial Spline for Solving Differential Equations of Fractional Order
In this paper, we implement new approximate techniques, the fractional lacunary interpolation by ... more In this paper, we implement new approximate techniques, the fractional lacunary interpolation by spline function for s lving differential equations of fractional order. Convergence a nalysis, existence and uniqueness are shown by several theo rems in the classes of C3 andC4 depend on the degree of spline polynomials. The numerical re sults demonstrates the errors bounds is quite validity and applicability of this method.
Computational Method for Fractional Differential Equations Using Nonpolynomial Fractional Spline
Mathematical Sciences Letters, 2016
In this paper, a new fractional spline method of non-polynomial form have been considered to solv... more In this paper, a new fractional spline method of non-polynomial form have been considered to solve special linear fractional boundary-value problems. Using this fractional spline function a few consistency relations are derived for computing approximations to the solution of the problem. Convergence analysis and error estimates of this methods are discussed. Numerical results are provided to demonstrate the superiority of our methods.
The discrete delta Caputo-Fabrizio fractional differences and sums are proposed to distinguish th... more The discrete delta Caputo-Fabrizio fractional differences and sums are proposed to distinguish their monotonicity analysis from the sense of Riemann and Caputo operators on the time scale Z. Moreover, the action of Q− operator and discrete delta Laplace transform method are also reported. Furthermore, a relationship between the discrete delta Caputo-Fabrizio-Caputo and Caputo-Fabrizio-Riemann fractional differences is also studied in detail. To better understand the dynamic behavior of the obtained monotonicity results, the fractional difference mean value theorem is derived. The idea used in this article is readily applicable to obtain monotonicity analysis of other discrete fractional operators in discrete fractional calculus.
AL-Rafidain Journal of Computer Sciences and Mathematics
The mechanism of thin liquid films on solid surfaces is fundamental to a wide variety of phenomen... more The mechanism of thin liquid films on solid surfaces is fundamental to a wide variety of phenomena such as surface coatings in paint. A mathematical model is constructed to describe the two dimensions of steady thin liquid films flow on an inclined plane with the use of lubrication approximation, we have applied Navier-Stokes equations in two dimensional coordinates for flow of incompressible fluid with the specified boundary conditions, and the solution of the film thickness equation has been drawn for flow for several inclination angles which modify the shape of the emerging patterns and also we derived the third order differential
In this paper, we construct numerical algorithms for solving Magnetohidrodynamics(MHD) free conve... more In this paper, we construct numerical algorithms for solving Magnetohidrodynamics(MHD) free convection flow rate whichhas been discussed in detail. It is observed that, for a nonlinear system of differential equation, the spline model of ninedegree is used, effectiveness and accuracy of this new method are presented. Several theorems relating the order of theninth spline to the saturation of the estimator are proved. Some results of consistency are given and an applicationMHD system is given.
In the paper a mathematical model is developed by using numerical solution to study the non stati... more In the paper a mathematical model is developed by using numerical solution to study the non stationary heat equation in one dimension. This model leads to incorporate a cooling system for a computer radiator. The result of the model is compared with the stationary heat transfer model. The simulation results show the performance of non stationary model in terms of variation of temperature.
Composition Fractional Integral Inequality for the Reiman-Liouville type with applications
Journal of Zankoy Sulaimani - Part A
In this work, some integral inequalities of fractional order of Riemann-Liouville type are establ... more In this work, some integral inequalities of fractional order of Riemann-Liouville type are established, which generalized some know inequalities for [8]. These can be used in the analysis of various problems in the theory of certain classes of fractional differential equations and fractional integral equations. Also, some applications for the fractional differential and integral equations are also indicated. Fractional integral inequalities, Holder's inequality
In this paper, consisted in finding the nonpolynomial spline function and generalized it by fract... more In this paper, consisted in finding the nonpolynomial spline function and generalized it by fractional order. Other propose of this function was interpolating spline fractional derivatives, with their effective applications to numerically solving fractional boundary value problems. We also discussed the rate of convergence of the method with fractional order. The error bounds and convergence of our difference schemes for nonpolynomial spline with fractional order are theoretically established, this is done by computer program with the aid of the Maptlab 13 for all the above prescribed methods, and the numerical results for boundary value problems are also presented.
International Journal of Open Problems in Computer Science and Mathematics, 2015
In this paper, a new fractional spline function of polynomial form with the idea of the lacunary ... more In this paper, a new fractional spline function of polynomial form with the idea of the lacunary interpolation is considered to find approximate solution for fractional differential equations (FDEs). The proposed method is applicable for α ∈ (0, 1], where α denotes the order of the fractional derivative in the Caputo sense. Convergence analysis of the method is considered. Some illustrative examples are presented and the obtained results reveal that the proposed technique is very effective, convenient and quite accurate to such considered problems. The study is conducted through illustrative examples and error analysis.
In this paper, a quintic spline interpolation algorithm presented for the solution of second orde... more In this paper, a quintic spline interpolation algorithm presented for the solution of second order initial value problems with a new class of the lacunary spline interpolation based on quintic C4-splines as an approximation to the exact solution of such problems. Convergence analysis of the presented spline function was discussed, stability analysis has been carried out and two examples were considered for the numerical illustration of the presented technique. The results show that the presented quintic spline function which interpolates the lacunary data was efficient and effective for solving such problems.
Abstract This paper presents a formulation and a study of three interpolatory fractional splines ... more Abstract This paper presents a formulation and a study of three interpolatory fractional splines these are in the class of ma, m = 2, 4, 6, a = 0.5. We extend fractional splines function with uniform knots to approximate the solution of fractional equations. The developed of spline method is to analysis convergence fractional order derivatives and estimating error bounds. We propose spline fractional method to solve fractional differentiation equations. Numerical example is given to illustrate the applicability and accuracy of the methods.
Numerical Approximation of Fractional Differential Equations with Fractional Spline Function. Journal of Zankoy Sulaimani – Part A (JZS-A), and it will be published in Vol.(17), No.(3), (2015)
In this paper, we consider a new suitable lacunary fractional interpolation with the idea of the ... more In this paper, we consider a new suitable lacunary fractional interpolation with the idea of the spline function of polynomial form, and the method applied to solve linear fractional differential equations. The results obtained are in good agreement with the exact analytical solutions and the numerical results presented by several examples, results also show that the technique introduced here is robust and easy to apply.
Uploads
Papers by Faraidun Salh