Study of Stability and Simulation for Nonlinear (k, ψ)-Fractional Differential Coupled Laplacian Equations with Multi-Point Mixed (k, ψ)-Derivative and Symmetric Integral Boundary Conditions

The (k,ψ)-fractional derivative based on the k-gamma function is a more general version of the Hilfer fractional derivative. It is widely used in differential equations to describe physical phenomena, population dynamics, and biological genetic memory problems. In this article, we mainly study the 4m+2-point symmetric integral boundary value problem of nonlinear (k,ψ)-fractional differential coupled Laplacian equations. The existence and uniqueness of solutions are obtained by the Krasnosel’skii fixed-point theorem and Banach’s contraction mapping principle. Furthermore, we also apply the calculus inequality techniques to discuss the stability of this system. Finally, three interesting examples and numerical simulations are given to further verify the correctness and effectiveness of the conclusions.