On the (k,φ)-Hilfer Langevin fractional coupled system having multi point boundary conditions and fractional integrals

In this manuscript, we investigate the (k,φ)-Hilfer Langevin fractional coupled system having multi point boundary conditions and fractional integrals. This study is crucial as it addresses the complexities of (k,φ)-Hilfer Langevin coupled system with multi point conditions, which have applications in many scientific and engineering fields. Unlike previous research, our work introduces novel techniques for analyzing this system, leading to more accurate and comprehensive results. The major findings include new existence and uniqueness theorems, along with improved stability conditions, which enhance the understanding and potential applications of these systems. We demonstrate the existence, uniqueness and different kinds of Ulam stability for our suggested model. We prove the uniqueness of the solution by utilizing Banach contraction mapping principle. The existence of solution is studied by using Krasnoselskii's fixed point theorem. We also explore the different types of Ulam stability under the specific conditions. We presented an example at the end to support our main results.