scholarly journals Sumudu Transform Method For Solving Fractional Differential Equations And Fractional Diffusion-wave Equation

2013 ◽  
Vol 06 (01) ◽  
pp. 79-84 ◽  
Author(s):  
R. Darzi ◽  
B. Mohammadzade ◽  
S. Mousavi ◽  
R. Beheshti
Keyword(s):  
Wave Equation ◽  
Differential Equations ◽  
Fractional Differential Equations ◽  
Fractional Diffusion ◽  
Transform Method ◽  
Diffusion Wave ◽  
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.

scholarly journals Series Solutions of High-Dimensional Fractional Differential Equations

Mathematics ◽  
2021 ◽  
Vol 9 (17) ◽  
pp. 2021
Author(s):  
Jing Chang ◽  
Jin Zhang ◽  
Ming Cai
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Salient Feature ◽  
Approximate Solutions ◽  
Series Solutions ◽  
Laplace Transform Method ◽  
Transform Method ◽  
Time Space ◽  
Sumudu Transform ◽  
Fractional Differential

In the present paper, the series solutions and the approximate solutions of the time–space fractional differential equations are obtained using two different analytical methods. One is the homotopy perturbation Sumudu transform method (HPSTM), and another is the variational iteration Laplace transform method (VILTM). It is observed that the approximate solutions are very close to the exact solutions. The solutions obtained are very useful and significant to analyze many phenomena, and the solutions have not been reported in previous literature. The salient feature of this work is the graphical presentations of the third approximate solutions for different values of order α.

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.

NONEXISTENCE OF SOLUTIONS RESULTS FOR CERTAIN FRACTIONAL DIFFERENTIAL EQUATIONS

2011 ◽  
Vol 16 (3) ◽  
pp. 488-497
Author(s):  
Mohamed Berbiche
Keyword(s):  
Differential Equations ◽  
Diffusion Equation ◽  
Fractional Differential Equations ◽  
Weak Solutions ◽  
Sufficient Conditions ◽  
Fractional Diffusion ◽  
Fractional Diffusion Equation ◽  
Convective Term ◽  
Nonexistence Of Solutions ◽  
Fractional Differential

This paper is meant to establish sufficient conditions for the nonexistence of weak solutions to nonlinear fractional diffusion equation in space and time with nonlinear convective term. The Fujita exponent is determined.

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