This analysis demonstrates unique solutions and stability in coupled systems of hybrid Langevin equations, indicating effective methods for complex differential equations.
This paper focuses on the study of a class of coupled systems of hybrid Langevin fractional pantograph differential equations involving the ψ-Caputo fractional derivative within Banach spaces. By applying Banach’s fixed-point theorem, we demonstrate the uniqueness of solutions to our coupled system. The existence of the solution is then shown using Dhage’s fixed-point theorem. Additionally, we analyze the stability in the sense of Ulam-Hyers and Ulam-Hyers-Rassias. Finally, we present an example to illustrate our results.
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Bouzid et al. (2025) studied this question.
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