NUMERICAL COMPUTATION OF FRACTIONAL PARTIAL DIFFERENTIAL EQUATIONS ARISING IN PHYSICS

J. SINGH, D. KUMAR, R. SWROOP, S. KUMAR

Abstract


In this article, we aim to propose a reliable numerical 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, invicid 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 problems. The proposed method may give better approximations which are uniformly valid for either small and large parameters or variables with highly accurate numerical solutions.


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