Existence and uniqueness solution of the Hammerstein type fractional equations via the fixed point theorems

The aim of this paper is to investigate the existence and uniqueness of solution for a class of nonlinear integro-differential equations known as Hammerstein type. We study fractional equations in the Banach space whose derivative is of the Caputo type. The existence of solution is studied by using the Schauder's fixed point theorem, and the uniqueness is established via a generalization of the Banach fixed point theorem. Finally, an example is given to illustrate the analytical findings.

کلیدواژه ها:

Fractional Hammerstein integro-differential equations ، Existence and uniqueness ، Schauder's fixed point theorem ، Banach fixed point theorem.