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 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 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 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.

scholarly journals Exact solutions for the differential equations in fractal heat transfer

2016 ◽  
Vol 20 (suppl. 3) ◽  
pp. 747-750 ◽  
Author(s):  
Chun-Yu Yang ◽  
Yu-Dong Zhang ◽  
Xiao-Jun Yang
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Exact Solutions ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Differential Transform Method ◽  
Transform Method ◽  
Differential Transform ◽  
Fractional Differential

In this article we consider the boundary value problems for differential equations in fractal heat transfer. The exact solutions of non-differentiable type are obtained by using the local fractional differential transform method.

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