Analytical approach to mixed integro-differential equations of fractional order using power series expansion principle

Accurate modeling of many natural phenomena utilizing fractional differential equations is essential to understand the structure, behavior, and construction of these problems. In this article, an analytic-numeric solution of mixed integro-differential equation of fractional-order is presented by using a residual power series expansion principle. This approach constructs to express the solutions in convergent series expansion form with effectively compatible components. Some basic properties for the RPS method are investigated. The numerical example is tested to illustrate the theoretical statements. Numerical results obtained indicate that the exact solution in good agreement with approximate solutions. The main features of the proposed method lie in that it can be directly applied for solving nonlinear fractional problems without the need for unphysical restrictive assumptions, such as linearization, perturbation, or guessing the initial data.