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The aim of this paper is to prove the existence and the uniqueness of the solution for some types of fractional non-local problems, namely the non-linear non-local initial value problems for fractional Fredholm-Volterra integro-differential equations. Also, the generalized Taylor expansion method is used to solve the non-local initial value problem that consists of the linear fractional Fredholm-Volterraintegro-differential equation together with the linear non-local initial condition with some illustrative examples.

The Generalized Taylor Expansion Method for Solving Some Types of Fractional Non-local Problems