Existence of Solutions and Hyers–Ulam Stability for a Coupled System of Nonlinear Fractional Differential Equations with <i>p</i>-Laplacian Operator

Abstract

In this paper, the existence and uniqueness of solutions to a coupled formally symmetric system of fractional differential equations with nonlinear p-Laplacian operator and nonlinear fractional differential-integral boundary conditions are obtained by using the matrix eigenvalue method. The Hyers–Ulam stability of the coupled formally symmetric system is also presented with certain growth conditions. By using the topological degree theory and nonlinear functional analysis methods, some sufficient conditions for the existence and uniqueness of solutions to this coupled formally symmetric system are established. Examples are provided to verify our results.

Keywords

• existence and uniqueness of solutions
• coupled system
• Hyers–Ulam stability
• topological degree theory
• p-Laplacian