Coupled systems of & psi;-Hilfer generalized proportional fractional nonlocal mixed boundary value problems

In this paper, we investigate a coupled system of Hilfer-type nonlinear proportional fractional differential equations supplemented with mixed multi-point and integro-multi-point boundary conditions. We used standard methods from functional analysis and especially fixed point theory. Two existence results are established using the Leray-Schauder's alternative and the Krasnosel'skii's fixed point theorem, while the existence of a unique solution is achieved via the Banach's contraction mapping principle. Finally, numerical examples are constructed to illustrate the main theoretical results. Our results are novel, wider in scope, produce a variety of new results as special cases and contribute to the existing literature on nonlocal systems of nonlinear & psi;-Hilfer generalized fractional proportional differential equations.

Automated summary

In this paper, a coupled system of Hilfer-type nonlinear proportional fractional differential equations supplemented with mixed multi-point and integro-multi-point boundary conditions is investigated. Standard methods from functional analysis, especially fixed point theory, are utilized. Two existence results are established using the Leray-Schauder's alternative and the Krasnosel'skii's fixed point theorem, while the existence of a unique solution is achieved via the Banach's contraction mapping principle. Numerical examples are presented to illustrate the main theoretical results. The results of this study are novel, have wider applicability, generate a variety of new results as special cases, and contribute to the existing literature on nonlocal systems of nonlinear & psi;-Hilfer generalized fractional proportional differential equations.