AN ITERATIVE METHOD FOR SOLVING TIME-FRACTIONAL PARTIAL DIFFERENTIAL EQUATIONS WITH PROPORTIONAL DELAYS

AN ITERATIVE METHOD FOR SOLVING TIME-FRACTIONAL PARTIAL DIFFERENTIAL EQUATIONS WITH PROPORTIONAL DELAYS

B. Mallick, P. K. Sahu, M. Routaray

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Abstract

This article deals with an iterative method which is a new formulation of Adomian decomposition method for solving time-fractional partial di erential equations (TFPDEs) with proportional delays. The fractional derivative taken here is in Caputo sense. Daftardar-Gejji and Jafari (2006) proposed this new technique where the non- linearity is de ned by using the new formula of Adomian polynomials and the new iterative formula (NIF) is independent of  . It does not require any discretization, per- turbation, or any restrictive parameters. It is shown that the NIF converges rapidly to the exact solutions. Three test problems have been illustrated in order to con rm the e ciency and validity of NIF.

Keywords

Adomian Polynomials, Partial di erential equations, Proportional delay, Fractional Calculus.