scholarly journals A note on Riccati-Bernoulli Sub-ODE method combined with complex transform method applied to fractional differential equations

2018 ◽  
Vol 7 (4) ◽  
pp. 279-285 ◽  
Author(s):  
Mahmoud A.E. Abdelrahman
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Dimensional Space ◽  
Nonlinear Ordinary Differential Equation ◽  
Transform Method ◽  
Fractional Equations ◽  
Dimensional Space Time ◽  
Ode Method ◽  
Fractional Differential ◽  
Partial Fractional Differential Equations

AbstractIn this paper, the fractional derivatives in the sense of modified Riemann–Liouville and the Riccati-Bernoulli Sub-ODE method are used to construct exact solutions for some nonlinear partial fractional differential equations via the nonlinear fractional Zoomeron equation and the (3 + 1) dimensional space-time fractional mKDV-ZK equation. These nonlinear fractional equations can be turned into another nonlinear ordinary differential equation by complex transform method. This method is efficient and powerful in solving wide classes of nonlinear fractional order equations. The Riccati-Bernoulli Sub-ODE method appears to be easier and more convenient by means of a symbolic computation system.

A note on exp-function method combined with complex transform method applied to fractional differential equations

2015 ◽  
Vol 4 (3) ◽  
pp. 201-208 ◽  
Author(s):  
Ozkan Guner ◽  
Ahmet Bekir ◽  
Halis Bilgil
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Fractional Differential Equations ◽  
Function Method ◽  
Fractional Derivatives ◽  
Nonlinear Ordinary Differential Equation ◽  
Transform Method ◽  
Fractional Equations ◽  
Fractional Differential ◽  
Partial Fractional Differential Equations

AbstractIn this article, the fractional derivatives in the sense of modified Riemann–Liouville and the exp-function method are used to construct exact solutions for some nonlinear partial fractional differential equations via the nonlinear fractional Liouville equation and nonlinear fractional Zoomeron equation. These nonlinear fractional equations can be turned into another nonlinear ordinary differential equation by complex transform method. This method is efficient and powerful in solving wide classes of nonlinear fractional order equations. The exp-function method appears to be easier and more convenient by means of a symbolic computation system.

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 NUMERICAL SOLUTION FOR TIME-FRACTIONAL MURRAY REACTION-DIFFUSION EQUATIONS VIA REDUCED DIFFERENTIAL TRANSFORM METHOD

2021 ◽  
Author(s):  
Muhammed Yiğider ◽  
Serkan Okur
Keyword(s):  
Differential Equations ◽  
Fractional Order ◽  
Fractional Differential Equations ◽  
Differential Transform Method ◽  
Reaction Diffusion Equations ◽  
Transform Method ◽  
Differential Transform ◽  
Fractional Differential ◽  
Reduced Differential Transform Method ◽  
Time Fractional Differential Equations

In this study, solutions of time-fractional differential equations that emerge from science and engineering have been investigated by employing reduced differential transform method. Initially, the definition of the derivatives with fractional order and their important features are given. Afterwards, by employing the Caputo derivative, reduced differential transform method has been introduced. Finally, the numerical solutions of the fractional order Murray equation have been obtained by utilizing reduced differential transform method and results have been compared through graphs and tables. Keywords: Time-fractional differential equations, Reduced differential transform methods, Murray equations, Caputo fractional derivative.

scholarly journals Lie symmetry analysis for the solution of first-order linear and nonlinear fractional differential equations

2018 ◽  
Vol 7 (2) ◽  
pp. 37 ◽  
Author(s):  
Mousa Ilie ◽  
Jafar Biazar ◽  
Zainab Ayati
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Lie Symmetry ◽  
Order Linear ◽  
Nonlinear Fractional Differential Equations ◽  
First Order ◽  
Fractional Equations ◽  
Fractional Differential ◽  
Linear And Nonlinear ◽  
Fractional Equation

Obtaining analytical or numerical solution of fractional differential equations is one of the troublesome and challenging issues among mathematicians and engineers, specifically in recent years. The purpose of this paper is to solve linear and nonlinear fractional differential equations such as first order linear fractional equation, Bernoulli, and Riccati fractional equations by using Lie Symmetry method, based on conformable fractional derivative. For each equation, some numerical examples are presented to illustrate the proposed approach.  

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