Stability Analysis of Coupled Hadamard Hybrid Fractional Differential Equations with Generalized Hybrid Boundary Conditions

Abstract The article is devoted to study a class of fractional order coupled hybrid Hadamard fractional differential equations having generalized hybrid Hadamard differential boundary conditions. If , a fourth‐order ordinary differential equation is obtained, which has many applications in coupled beam vibration, nanofluid flow and many fields of science and engineering. The existence theory of the coupled hybrid problem is established using a simple integral method. In addition, uniqueness and at least one solution of the proposed coupled system will be established through the Banach contraction principle and the hybrid fixed point theorem, respectively. For stability, the corresponding perturb integral equations of the suggested model are explained, and it is shown that such a problem is stable in the Hyers–Ulam sense under certain conditions. At the end of the analysis, two examples are explored to verify all the results and illustrate the solution behavior through graphs.