Stability and existence the solution for a coupled system of hybrid fractional differential equation with uniqueness

Abstract

In this literature, we are investigating the existence and uniqueness of solutions for a coupled system of hybrid differential equations with p-Laplacian operator involving the fractional derivatives Caputo and Riemann–Liouville derivatives of various orders. For this purpose, the proposed problem will be converted into integral equations by using two Green functions for ], where . The existence of a solution is proved by using topological degree and Leray–Schauder fixed point theorems. Uniqueness of solution is obtained with the help of Banach principle. Some adequate conditions for Hyers–Ulam- stability of the solution also are investigated. To verify the results. An expressive example will be presented to clarify the results.

Keywords

• topological degree theorem
• fractional differential
• hyers–ulam stability
• caputo’s fractional derivative and riemann–liouville derivatives