On using coupled fixed-point theorems for mild solutions to coupled system of multipoint boundary value problems of nonlinear fractional hybrid pantograph differential equations

The aims of this manuscript is to establish conditions for obtaining mild solutions to a coupled systems of multipoint boundary value problems (BVPs) of fractional order hybrid differential equations (FHDEs) with nonlinear perturbations of second type. In the concerned problem, we consider a proportional type delay that represent a famous class of differential equation called pantograph equations. Hence, we establish sufficient conditions for at least one mild solution to the coupled system of fractional hybrid pantograph differential equations (FHPDEs) by using Burton and couple-type fixed-point theorems. We also provide examples to show the applicability of our results.