title: Approximate series solution of multi-dimensional, time fractional-order (heat-like) diffusion equations using FRDTM.
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.
authors.affiliation: Department of Applied Mathematics , Babasaheb Bhimrao Ambedkar University, Lucknow 226025 , Uttar Pradesh, India.
authors.forename: Brajesh K
authors.initials: BK
authors.lastname: Singh
authors.affiliation: ISRO Telemetry , Tracking and Command Network (ISTRAC) , Bangalore, Karnataka 560058, India.
authors.forename: Vineet K
authors.initials: VK
authors.lastname: Srivastava
keywords: Caputo time-fractional derivative; Mittag–Leffler function; exact solution; fractional-order reduced differential transform method; multi-dimensional diffusion equation