A Study on Solving Fractional Volterra Integral Equations with Müntz Orthogonal Functions

In this paper, Müntz orthogonal functions are employed for the numerical solution of fractional Volterra integral equations. These functions are defined on the interval [0, 1] and possess simple and distinct real roots, providing the best unique approximation for functions in L2(0, 1). The Riemann–Liouville fractional integral operator is defined for these functions to reduce computational complexity and increase the solution speed. The error bound of the method is also determined. The numerical examples presented demonstrate the superiority of the proposed method compared to other existing approaches for the numerical solution of fractional Volterra integral equations.