Some Approximate Solutions of Fractional Integro-Differential Equations

The main objective of this thesis is to introduce fractional integrodifferential equations using a modified type of operators, which consists of the same order fractional differentiation and fractional integration. Also, the objective of this work is to study and prove the existence theorems of a unique solution of the fractional integro-differential equations, then studying the approximate solutions of such type of the equations using the collocation method, the least square method, the Adomian decomposition method and the modification of Adomian's polynomials method which are presented with the illustrative examples and comparised between the results.