Some Approximated Methods for Solving Fractional Non-Local Problems

The aim of this work is to study some types of the fractional non-local problems. These types are the fractional non-local initial value problems that consist of the non-linear fractional Fredholm, Volterra, Fredholm-Volterra integro-differential equations together with the non-linear non-local initial conditions of the integral type.This study includes the existence and the uniqueness of the solution for the non-linear fractional Fredholm-Volterra integro-differential equations together with the non-linear non-local initial conditions.Also, Laplace transform method is used to solve special types of the linear fractional non-local problems with some illustrative examples.Moreover, the generalized Taylor expansion method is presented to solve the non-local initial value problems that consist of the linear fractional FredholmVolterra
integro-differential equations together with the linear non-local initial conditions with some illustrative examples.