On solution of BG−Volterra integral equations

Abstract

In this study, we center upon obtaining the solution of linear bigeometric Volterra integral equations of the second kind in the sense of bigeometric calculus. The method of successive substitutions and resolvent kernel method are applied for solving the linear bigeometric Volterra integral equations of the second kind by using the concept of bigeometric integral. The necessary conditions for the bigeometric continuity and the uniqueness of the solution of linear bigeometric Volterra integral equations of the second kind are given in these methods. Finally, some numerical examples are presented to explain the procedure of the method of successive substitutions and resolvent kernel method.