Solution of nonlinear fractional differential equations using the homotopy perturbation Sumudu transform method

2014 ◽  
Vol 8 ◽  
pp. 2195-2210 ◽  
Author(s):  
Eltayeb A. Yousif ◽  
Sara H. M. Hamed
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Transform Method ◽  
Nonlinear Fractional Differential Equations ◽  
Homotopy Perturbation ◽  
Sumudu Transform ◽  
Fractional Differential

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.

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.

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.

Toward a New Algorithm for Nonlinear Fractional Differential Equations

2013 ◽  
Vol 5 (2) ◽  
pp. 222-234
Author(s):  
Fadi Awawdeh ◽  
S. Abbasbandy
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Homotopy Analysis Method ◽  
Analytical Techniques ◽  
Analytic Solutions ◽  
Analysis Method ◽  
Transform Method ◽  
Nonlinear Fractional Differential Equations ◽  
Homotopy Analysis ◽  
Fractional Differential

AbstractThis paper is concerned with the development of an efficient algorithm for the analytic solutions of nonlinear fractional differential equations. The proposed algorithm Laplace homotopy analysis method (LHAM) is a combined form of the Laplace transform method with the homotopy analysis method. The biggest advantage the LHAM has over the existing standard analytical techniques is that it overcomes the difficulty arising in calculating complicated terms. Moreover, the solution procedure is easier, more effective and straightforward. Numerical examples are examined to demonstrate the accuracy and efficiency of the proposed algorithm.

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.

ELZAKI PROJECTED DIFFERENTIAL TRANSFORM METHOD FOR FRACTIONAL ORDER SYSTEM OF LINEAR AND NONLINEAR FRACTIONAL PARTIAL DIFFERENTIAL EQUATION

Fractals ◽  
2018 ◽  
Vol 26 (03) ◽  
pp. 1850041 ◽  
Author(s):  
DIANCHEN LU ◽  
MUHAMMAD SULEMAN ◽  
JI HUAN HE ◽  
UMER FAROOQ ◽  
SAMAD NOEIAGHDAM ◽  
...  
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Series Solution ◽  
Differential Transform Method ◽  
Order System ◽  
Transform Method ◽  
Nonlinear Fractional Differential Equations ◽  
Differential Transform ◽  
Fractional Differential ◽  
Linear And Nonlinear

The pivotal aim of this paper is to propose an efficient computational technique, namely, Elzaki fractional projected differential transform method (EFPDTM) to solve the system of linear and nonlinear fractional differential equations. In the EFPDTM process, we investigate the behavior of independent variables for convergent series solution in admissible range. The EFPDTM manipulates and controls the series solution, which rapidly converges to the exact solution in a large admissible domain in a very efficient way. The solution procedure and explanation show the flexible efficiency of the EFPDTM, compared to the other existing classical techniques for solving the system of linear and nonlinear fractional differential equations.

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