Solution of a class of Volterra integral equations with singular and weakly singular kernels

A class of Volterra integral equations are solved in this paper, where the involved kernel may be weakly singular, singular, and hypersingular. For various cases, existence and uniqueness of such Volterra integral equations are established. Furthermore, by reducing such equations to ordinary differential equations, analytic solutions have been determined explicitly. When restricting the solutions to certain special function classes, the number of suitable solutions is given.