Approximate Analytical Solutions of Fractional Perturbed Diffusion Equation by Reduced Differential Transform Method and the Homotopy Perturbation Method. (1st July 2013)

• Record Type: Journal Article
• Authors: Cui, Zhoujin; Mao, Zisen; Yang, Sujuan; Yu, Pinneng
• Other Names: Wen Guanghui Academic Editor.
• Is Part Of: Mathematical problems in engineering. Volume 2013(2013)
• Publication Date: 2013-07-01
• Subjects: Engineering mathematics -- Periodicals; 510.2462
• DOI: 10.1155/2013/186934
• Languages: English
• ISSNs: 1024-123X

Abstract

Abstract : The approximate analytical solutions of differential equations with fractional time derivative are obtained with the help of a general framework of the reduced differential transform method (RDTM) and the homotopy perturbation method (HPM). RDTM technique does not require any discretization, linearization, or small perturbations and therefore it reduces significantly the numerical computation. Comparing the methodology (RDTM) with some known technique (HPM) shows that the present approach is effective and powerful. The numerical calculations are carried out when the initial conditions in the form of periodic functions and the results are depicted through graphs. The two different cases have studied and proved that the method is extremely effective due to its simplistic approach and performance.