USING A PRIOR ESTIMATE METHOD TO INVESTIGATE SEQUENTIAL HYBRID FRACTIONAL DIFFERENTIAL EQUATIONS

In this paper, our main objective is to develop the conditions that assure the existence of solution to a system of boundary value problems (BVPs) of sequential hybrid fractional differential equations (SHFDEs). The problem is considered under the nonlinear boundary conditions. Nonlinear functions involved in the considered system of SHFDEs are continuous and satisfy the growth conditions. We convert the system of SHFDEs to the system of fixed points problem by using the technique of the topological degree theory also called prior estimate method. We establish sufficient conditions that guarantee the existence and uniqueness of positive solution to the system under consideration. Moreover, suitable results are also developed for the Hyers–Ulam stability analysis for the solution of the considered problem. An example is also included to reveal our main result.