scholarly journals The Use of Sumudu Transform for Solving Certain Nonlinear Fractional Heat-Like Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Abdon Atangana ◽  
Adem Kılıçman
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Variable Coefficients ◽  
Fractional Partial Differential Equations ◽  
Science And Engineering ◽  
Transform Method ◽  
Homotopy Perturbation ◽  
Sumudu Transform ◽  
Fractional Differential ◽  
Linear And Nonlinear

We make use of the properties of the Sumudu transform to solve nonlinear fractional partial differential equations describing heat-like equation with variable coefficients. The method, namely, homotopy perturbation Sumudu transform method, is the combination of the Sumudu transform and the HPM using He’s polynomials. This method is very powerful, and professional techniques for solving different kinds of linear and nonlinear fractional differential equations arising in different fields of science and engineering.

HOMOTOPY PERTURBATION TRANSFORM METHOD FOR SOLVING SYSTEMS OF NONLINEAR PARTIAL FRACTIONAL DIFFERENTIAL EQUATIONS

2021 ◽  
Vol 21 (2) ◽  
pp. 355-364
Author(s):  
ABDELKADER KEHAILI ◽  
ABDELKADER BENALI ◽  
ALI HAKEM
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Fractional Differential Equations ◽  
Efficient Method ◽  
Fractional Partial Differential Equations ◽  
Transform Method ◽  
Homotopy Perturbation ◽  
Computational Work ◽  
Fractional Differential ◽  
Partial Fractional Differential Equations

In this paper, we apply an efficient method called the Homotopy perturbation transform method (HPTM) to solve systems of nonlinear fractional partial differential equations. The HPTM can easily be applied to many problems and is capable of reducing the size of computational work.

scholarly journals Homotopy Perturbation Transform method for solving the partial and the time-fractional differential equations with variable coefficients

2020 ◽  
Vol 26 (1) ◽  
pp. 35-55
Author(s):  
Abdelkader Kehaili ◽  
Ali Hakem ◽  
Abdelkader Benali
Keyword(s):  
Differential Equations ◽  
Laplace Transform ◽  
Fractional Derivative ◽  
Exact Solutions ◽  
Fractional Differential Equations ◽  
Variable Coefficients ◽  
Transform Method ◽  
Homotopy Perturbation ◽  
Fractional Differential ◽  
Time Fractional Differential Equations

In this paper, we present the exact solutions of the Parabolic-like equations and Hyperbolic-like equations with variable coefficients, by using Homotopy perturbation transform method (HPTM). Finally, we extend the results to the time-fractional differential equations. Keywords: Caputo’s fractional derivative, fractional differential equations, homotopy perturbation transform method, hyperbolic-like equation, Laplace transform, parabolic-like equation.

Numerical and analytical solutions of nonlinear differential equations involving fractional operators with power and Mittag-Leffler kernel

2018 ◽  
Vol 13 (1) ◽  
pp. 13 ◽  
Author(s):  
H. Yépez-Martínez ◽  
J.F. Gómez-Aguilar
Keyword(s):  
Differential Equations ◽  
Fractional Derivative ◽  
Fractional Differential Equations ◽  
Fractional Derivatives ◽  
Nonlinear Differential Equations ◽  
Fractional Operators ◽  
Transform Method ◽  
Homotopy Perturbation ◽  
Fractional Differential ◽  
Derivative Order

Analytical and numerical simulations of nonlinear fractional differential equations are obtained with the application of the homotopy perturbation transform method and the fractional Adams-Bashforth-Moulton method. Fractional derivatives with non singular Mittag-Leffler function in Liouville-Caputo sense and the fractional derivative of Liouville-Caputo type are considered. Some examples have been presented in order to compare the results obtained, classical behaviors are recovered when the derivative order is 1.

scholarly journals A new approach for solving systems of fractional differential equations via natural transform

2016 ◽  
Vol 12 (1) ◽  
pp. 5797-5804 ◽  
Author(s):  
A. S Abedl Rady ◽  
S. Z Rida ◽  
A. A. M Arafa ◽  
H. R Abedl Rahim
Keyword(s):  
Nonlinear Systems ◽  
Differential Equations ◽  
Fractional Differential Equations ◽  
Variational Iteration Method ◽  
New Method ◽  
Transform Method ◽  
Variational Iteration ◽  
Fractional Differential ◽  
Linear And Nonlinear ◽  
Linear And Nonlinear Systems

In this paper, A new method proposed and coined by the authors as the natural variational iteration  transform method(NVITM) is utilized to solve linear and nonlinear systems of fractional differential equations. The new method is a combination of natural transform method and variational iteration method. The solutions of our modeled systems are calculated in the form of convergent power series with easily computable components. The numerical results shows that the approach is easy to implement and accurate when applied to various linear and nonlinear systems of fractional differential equations.

scholarly journals A Hybrid Natural Transform Homotopy Perturbation Method for Solving Fractional Partial Differential Equations

2016 ◽  
Vol 2016 ◽  
pp. 1-7 ◽  
Author(s):  
Shehu Maitama
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Perturbation Method ◽  
Analytical Method ◽  
Homotopy Perturbation Method ◽  
Fractional Partial Differential Equations ◽  
Partial Differential ◽  
Transform Method ◽  
Homotopy Perturbation ◽  
Linear And Nonlinear

A hybrid analytical method for solving linear and nonlinear fractional partial differential equations is presented. The proposed analytical approach is an elegant combination of the Natural Transform Method (NTM) and a well-known method, Homotopy Perturbation Method (HPM). In this analytical method, the fractional derivative is computed in Caputo sense and the nonlinear term is calculated using He’s polynomial. The proposed analytical method reduces the computational size and avoids round-off errors. Exact solution of linear and nonlinear fractional partial differential equations is successfully obtained using the analytical method.

An efficient hybrid computational technique for solving nonlinear local fractional partial differential equations arising in fractal media

2018 ◽  
Vol 7 (3) ◽  
pp. 229-235 ◽  
Author(s):  
Amit Prakash ◽  
Hardish Kaur
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Planck Equation ◽  
Computational Technique ◽  
Fractional Partial Differential Equations ◽  
Partial Differential ◽  
Transform Method ◽  
Homotopy Perturbation ◽  
Fractal Media ◽  
Sumudu Transform

AbstractIn present work, nonlinear fractional partial differential equations namely transport equation and Fokker-Planck equation involving local fractional differential operators, are investigated by means of the local fractional homotopy perturbation Sumudu transform method. The proposed method is a coupling of homotopy perturbation method with local fractional Sumudu transform and is used to describe the non-differentiable problems. Numerical simulation results are projected to show the efficiency of the proposed technique.

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