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.