Journal of the Vol. 35, pp. 439-459, 2016 Nigerian Mathematical Society c Nigerian Mathematical Society NUMERICAL COMPUTATION OF FRACTIONAL PARTIAL DIFFERENTIAL EQUATIONS ARISING IN PHYSICS J. SINGH, D. KUMAR 1 , R. SWROOP AND S. KUMAR ABSTRACT. In this article, we aim to propose a reliable numer- ical algorithm based on homotopy analysis transform method for solving various kinds of linear and nonlinear time-fractional partial differential equations arising in physics. The method is exemplified by linear and nonlinear time- fractional heat-like, in- vicid Burgers and fifth orders KdV equations arising in the study of thermodynamics, fluid mechanics and quantum mechanics respectively. We investigate the influence of the convergence- control parameter  that provides us, a simple way to guarantee the convergence of series solution of linear and nonlinear prob- lems. The proposed method may give better approximations which are uniformly valid for either small and large parameters or variables with highly accurate numerical solutions. Keywords and phrases: Fractional heat-like equations, Frac- tional invicid Burgers equation, Fifth orders KdV equations, Laplace transform, Homotopy analysis transform method 2010 Mathematical Subject Classification: 34A08, 35A20, 35A22 1. INTRODUCTION Fractional differential equations have garnered a lot of attention and appreciation due to their ability to facilitate an exact description of different linear and nonlinear phenomena’s. There are many books and definitions that develop and investigate about the fractional or- der integrations and differentiations [1-4]. During the last decades, number of powerful computational techniques were introduced and investigated by many research workers for obtaining exact and ap- proximate solutions of fractional equations [5-11]. This paper adopts homotopy analysis transform method (HATM) to solve higher dimensional initial value problems of constant and variable coefficients, linear and nonlinear, partial fractional dif- ferential equations occurring in scientific and technological fields. Received by the editors February 01, 2016; Revised: September 24, 2016; Accepted: October 31, 2016 1 Corresponding author 439