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In this paper, we have used generalized differential transform method in obtaining a general recurrence relation for determining the solutions of time fractional diffusion equation with external force and absorbent term. Diffusion equations play an improtant part in energy transfer problems. Inclusion of fractional derivatives bring the non-locality aspect into the physical system containing this equation. The obtained relation will help us to solve such equations with various external forces and initial conditions. Three illustrative examples have been discussed. Key–Words: Time-fractional diffusion equation, External force, Reaction term, Absorbent term, Generalized differential transform method, Mittag-Leffler function Received: July 15, 2020. Revised: August 31, 2020. Accepted: September 4, 2020. Published: September 9, 2020.

wseas transactions on systems

An Analytical Solution of a Time-fractional Diffusion Equation Withexternal Force and Absorbent Term by Generalized Two-dimensional differential Transform Method