The aim of this work is to discuss the solvability a boundary value problem for nonlinear integro-differential equation. First, we derive an equivalent Fredholm integral equation (NFIE) problem. Second, prove existence solution NFIE using Krasnosel’skii fixed point theorem under verifying some sufficient conditions. Third, solve numerically and study convergence rate via methods based upon appl...

The Sumudu decomposition method was used and developed in this paper to find approximate solutions for a general form of fractional integro-differential equation Volterra Fredholm types. Caputo definition deal with derivatives. As the under consideration depends mainly on writing non-linear terms, which are often found inside kernel integral equation, it Adomian’s polynomials well-known way. Af...

We construct the algebra of integro-differential operators over an ordinary integro-differential algebra directly in terms of normal forms. In the case of polynomial coefficients, we use skew polynomials for defining the integro-differential Weyl algebra as a natural extension of the classical Weyl algebra in one variable. Its normal forms, algebraic properties and its relation to the localizat...