scholarly journals A modification of the reduced differential transform method for fractional calculus

2018 ◽  
Vol 22 (4) ◽  
pp. 1871-1875 ◽  
Author(s):  
Kang-Le Wang ◽  
Kang-Jia Wang
Keyword(s):  
Heat Transfer ◽  
Fractional Calculus ◽  
Differential Transform Method ◽  
New Method ◽  
Transform Method ◽  
Numerical Examples ◽  
Differential Transform ◽  
Transfer Equations ◽  
Reduced Differential Transform Method

In this paper, the reduced differential transform method is modified and successfully used to solve the fractional heat transfer equations. The numerical examples show that the new method is efficient, simple, and accurate.

scholarly journals The Telegraph Equation and Its Solution by Reduced Differential Transform Method

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Vineet K. Srivastava ◽  
Mukesh K. Awasthi ◽  
R. K. Chaurasia ◽  
M. Tamsir
Keyword(s):  
Telegraph Equation ◽  
Differential Transform Method ◽  
Mathematical Technique ◽  
Science And Engineering ◽  
Transform Method ◽  
Numerical Examples ◽  
One Dimensional ◽  
Wide Range ◽  
Differential Transform ◽  
Reduced Differential Transform Method

One-dimensional second-order hyperbolic telegraph equation was formulated using Ohm’s law and solved by a recent and reliable semianalytic method, namely, the reduced differential transform method (RDTM). Using this method, it is possible to find the exact solution or a closed approximate solution of a differential equation. Three numerical examples have been carried out in order to check the effectiveness, the accuracy, and convergence of the method. The RDTM is a powerful mathematical technique for solving wide range of problems arising in science and engineering fields.

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 Solving a Higher-Dimensional Time-Fractional Diffusion Equation via the Fractional Reduced Differential Transform Method

2021 ◽  
Vol 5 (4) ◽  
pp. 168
Author(s):  
Salah Abuasad ◽  
Saleh Alshammari ◽  
Adil Al-rabtah ◽  
Ishak Hashim
Keyword(s):  
Approximate Solutions ◽  
Fractional Diffusion ◽  
Differential Transform Method ◽  
Diffusion Equations ◽  
Caputo Fractional Derivatives ◽  
Transform Method ◽  
Fractional Diffusion Equations ◽  
Higher Dimensional ◽  
Differential Transform ◽  
Reduced Differential Transform Method

In this study, exact and approximate solutions of higher-dimensional time-fractional diffusion equations were obtained using a relatively new method, the fractional reduced differential transform method (FRDTM). The exact solutions can be found with the benefit of a special function, and we applied Caputo fractional derivatives in this method. The numerical results and graphical representations specified that the proposed method is very effective for solving fractional diffusion equations in higher dimensions.

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