CONSTRUCTION OF EXPLICIT SOLUTION FORMULAS FOR VOLTERRA INTEGRAL EQUATIONS VIA THE METHOD OF SUCCESSIVE APPROXIMATIONS

Abstract

Integral equations have numerous applications in science and engineering, as they model phenomena with memory effects or global interactions. Various methods have been developed for solving integral equations, including the method of successive approximations, series methods, fixed point theorems, integral transform techniques, and numerical approaches. In this paper, we investigate several classes of integral equations that commonly arise in the study of differential equations involving derivatives of non-integer order. By applying the method of successive approximations, we construct explicit solution formulas for these integral equations. The proposed method can be extended to other classes of integral equations. Moreover, the obtained solutions provide a basis for studying qualitative properties of solutions to nonlinear fractional integro-differential equations.