Iterative Decomposition Method for solving Singular differential, Singular integral and Singular integro-differential equations

Abstract

In the paper, on Iterative Decomposition method is proposed to approximate analytical solution of Singular Differential, Integral and Integro-differential equations the method involves deriving a formula for finding the fractional integrals of fractional differential and integro-differential equations as the inverse operators of the respective differential operator. A recursive formula, devoid of linearization or discretization was derived, which uses the reduces at previous points to obtained the next iteration. The solution was then presented as an infinite series of easily comparable terms which converge, even for every few terms. The convergence of the method is established.