Approximate series solution of multi-dimensional, time fractional-order (heat-like) diffusion equations using FRDTM. Issue 4 (April 2015)

• Record Type: Journal Article
• Authors: Singh, Brajesh K.; Srivastava, Vineet K.
• Is Part Of: Royal Society open science. Volume 2:Issue 4(2015)
• Publication Date: 2015-04
• Subjects: multi-dimensional diffusion equation -- Caputo time-fractional derivative -- Mittag–Leffler function -- fractional-order reduced differential transform method -- exact solution; Science -- Periodicals; 500
• DOI: 10.1098/rsos.140511
• Languages: English
• ISSNs: 2054-5703

Abstract

Abstract : The main goal of this paper is to present a new approximate series solution of the multi-dimensional (heat-like) diffusion equation with time-fractional derivative in Caputo form using a semi-analytical approach: fractional-order reduced differential transform method (FRDTM). The efficiency of FRDTM is confirmed by considering four test problems of the multi-dimensional time fractional-order diffusion equation. FRDTM is a very efficient, effective and powerful mathematical tool which provides exact or very close approximate solutions for a wide range of real-world problems arising in engineering and natural sciences, modelled in terms of differential equations.