تفاصيل الرسالة العلمية

This thesis is focused at constructing an analytic-numeric solution based on fractional power series expansion for the fractional integro-differential equations of Fredholm-Volterra type by using residual power series (RPS) approach. The FRPS technique is combining the generalized Taylor series formula with the residual error functions. The methodology is based on the construction of a fractional power series expansion in convergent form and apparent sequences of the solution with surely computable components without any restrictive hypotheses. Illustrative numerical examples are included to demonstrate efficiency, accuracy, and applicability of the RPS method. Numerical results obtained indicate that the exact solution in good agreement with approximate solutions