A note on linear non-Newtonian Volterra integral equations

Abstract

In this study, the Volterra integral equations are defined in the non-Newtonian calculus with the aid of *-integral. The focus of this study is obtaining the solution of linear non-Newtonian integral equations. The *-resolvent kernel method, successive approximations method and Adomian decomposition method are applied for solving non-Newtonian integral equations in the non-Newtonian sense. Some numerical examples are presented to explain the procedure of these methods. Finally, a model that describes a type of the exponential growth model is proposed in the sense of non-Newtonian calculus as an example.