An iterative method for solving time-fractional partial differential equations with proportional delays

Abstract

This article deals with an iterative method which is a new formulation of Adomian decomposition method for solving time-fractional partial differential 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 nonlinearity is defined by using the new formula of Adomian polynomials and the new iterative formula (NIF) is independent of λ. It does not require any discretization, perturbation, 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 confirm the efficiency and validity of NIF.