Existence and stability of solution to a toppled systems of differential equations of non-integer order

Abstract

The aim of this paper is developing conditions that guarantee the existence of a solution to a toppled system of differential equations of noninteger order with fractional integral boundary conditions where the nonlinear functions involved in the considered system are continuous and satisfy some growth conditions. We convert the system of differential equations to a system of fixed point problems for condensing mapping. With the help of techniques of the topological degree theory, we establish adequate conditions that ensure the existence and uniqueness of positive solutions to a toppled system under consideration. Moreover, some conditions are also developed for the Hyers-Ullam stability of the solution to the system under consideration. Finally, to demonstrate the obtained results, we provide an example.