Stability analysis of p-fractional Schrodinger–Kirchhoff equations with electromagnetic fields and Hardy–Littlewood–Sobolev nonlinearity

Abstract

In this paper, we investigate the existence, uniqueness, and stability of solutions to a p-fractional Schrodinger–Kirchhoff equation incorporating electromagnetic fields and Hardy–Littlewood–Sobolev type nonlinearity. We reformulate the equation using the Green’s function technique to effectively address its nonlocal and nonlinear structure. Existence of solutions is established via the Banach fixed-point theorem, while uniqueness is proven using Krasnoselskii’s fixed-point theorem. Stability is examined through an appropriate application of Gronwall’s inequality. To support the theoretical results, an illustrative example is provided, accompanied by a MATLAB-generated graph that visually demonstrates the solution’s behavior. These findings enhance the analytical framework for fractional quantum models characterized by nonlocal interactions and complex external field effects.