Hyers–Ulam stability and existence of solution for hybrid fractional differential equation with p-Laplacian operator

•We have studied of the existence and uniqueness of solutions of hybrid fractional differential equations (FDEs) with the p-Laplacian operator.•We have established the existence of solutions of hybrid FDEs by using Krasnoselskii’s fixed point theorem.•We have established the uniqueness of solutions of hybrid FDEs by using Banach contraction mapping principle.•An illustrative example of our main results is also presented. This manuscript studies the hybrid fractional differential equations (FDEs) with the p-Laplacian operator. The main aim of this research work is to establish the existence and uniqueness(EU) results as well as to analyze the Hyers-Ulam (HU) stability for hybrid FDEs involving fractional derivatives of various orders with the p-Laplacian operator. We will convert the given problem into an equivalent integral form of hybrid FDEs for EU results with the help of the green function. The existence of solution(ES) is investigated using a fixed point theorem, and the uniqueness of the solution is obtained using the Banach contraction mapping principle technique. The dynamical systems and functional analysis tools are applied to analyze the HU stability result. An example is given to demonstrate our obtained results.