Solving fuzzy fractional differential equations by a generalized differential transform method

SeMA Journal ◽  
2015 ◽  
Vol 73 (2) ◽  
pp. 149-170 ◽  
Author(s):  
A. Rivaz ◽  
O. S. Fard ◽  
T. A. Bidgoli
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Differential Transform Method ◽  
Transform Method ◽  
Differential Transform ◽  
Fractional Differential ◽  
Generalized Differential ◽  
Fuzzy Fractional Differential Equations

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 A new method solving local fractional differential equations in heat transfer

2019 ◽  
Vol 23 (3 Part A) ◽  
pp. 1663-1669
Author(s):  
Yong-Ju Yang
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Fractional Differential Equations ◽  
Differential Transform Method ◽  
New Method ◽  
Transform Method ◽  
Variational Iteration ◽  
Differential Transform ◽  
Differential Operation ◽  
Fractional Differential

In this article, a new method, which is coupled by the variational iteration and reduced differential transform method, is proposed to solve local fractional differential equations. The advantage of the method is that the integral operation of variational iteration is transformed into the differential operation. One test examples is presented to demonstrate the reliability and efficiency of the proposed method.

scholarly journals Solving Coupled Fractional Differential Equations Using Differential Transform Method.

2021 ◽  
Vol 12 (4) ◽  
pp. 535-539
Author(s):  
Mridula Purohit, Et. al.
Keyword(s):  
Differential Equations ◽  
Fractional Order ◽  
Fractional Differential Equations ◽  
Analytical Solutions ◽  
Differential Transform Method ◽  
Transform Method ◽  
Coupled Equations ◽  
Fractional Oscillator ◽  
Differential Transform ◽  
Fractional Differential

This paper presents the solution of coupled equations which are of fractional order using differential transform method. In this paper we extend the scope of differential transform method to system of fractional differential equations so that we get the analytical solutions. The coupled fractional differential equations of a physical system, namely, coupled fractional oscillator with some applications is given via differential transform method. Here we introduce the solution of coupled oscillation of equal fractional order which can be enhanced to unequal fractional order.

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.

Analytical Approach to Time-Fractional Partial Differential Equations in Fluid Mechanics

2011 ◽  
Vol 347-353 ◽  
pp. 463-466
Author(s):  
Xue Hui Chen ◽  
Liang Wei ◽  
Lian Cun Zheng ◽  
Xin Xin Zhang
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Fluid Mechanics ◽  
Approximate Solutions ◽  
Differential Transform Method ◽  
Fractional Partial Differential Equations ◽  
Partial Differential ◽  
Transform Method ◽  
Differential Transform ◽  
Generalized Differential

The generalized differential transform method is implemented for solving time-fractional partial differential equations in fluid mechanics. This method is based on the two-dimensional differential transform method (DTM) and generalized Taylor’s formula. Results obtained by using the scheme presented here agree well with the numerical results presented elsewhere. The results reveal the method is feasible and convenient for handling approximate solutions of time-fractional partial differential equations.

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