A Numerical Study of a Fractional Integro-Differential Equations Using Fractional Quadratic Spline Methods

In this paper, a numerical method based on fractional spline methods (FSM) is proposed for solving fractional integro-differential equations (FIDEs). The main idea is to approximate the unknown solution by using fractional spline basis functions, which provide good flexibility for representing functions with weak singularities and memory-dependent behavior. The fractional derivative and integral terms are transformed into a system of algebraic equations by applying suitable collocation points. The obtained system is then solved to approximate the solution of the fractional integro-equation. The accuracy and efficiency of the proposed method are demonstrated through numerical examples. The results show that the fractional spline approach is simple and effective for solving fractional integro differential equations.