Laplace Adomian decomposition method for integro differential equations on time scale

Abstract

The aim of this work is to probe the Laplace Adomian decomposition method (LADM) for some certain linear and non-linear integro-differential equations on an arbitrary time scales. Although, several researchers have treated integro-differential equations (linear/nonlinear) utilizing different techniques, but most of them were based on classical calculus. In particular, [10] have catered the integro-differential equations on time scale using Adomian decomposition method (ADM). Whereas [28] have entertained the initial value problems with ADM on time scales. However, there exist no piece of work in literature that addressed integro-differential equations using LADM on time scales. Hence, in this work, that gap is covered. Moreover, the proposed method on time scale is effective in the sense that it mitigates the integration steps which otherwise come while solving with ADM. Lastly, examples and solutions in Sections 3 and 4 that exactly match those found by ADM are used to validate the suggested approach.