On the study of nonlinear sequential fractional integro-differential equation with nonseparated boundary conditions

The aim of this paper is to study the existing results of nonlinear sequential fractional integro-differential equations with nonseparated boundary conditions. In this work, we consider a nonlinear problem and general boundary conditions. This extension introduces mathematical difficulties which we will overcome by using fixed-point techniques. For this, we rewrite the nonlinear boundary problem as a fixed point one involving two operators. Then, we show that these operators satisfy the conditions of the Krasnoselskii theorem. An example is given to illustrate our result.

کلیدواژه ها:

Fractional differential equation ، Krasnoselskii fixed point theorem ، nonseparated boundary conditions