Analysis of q‐fractional coupled implicit systems involving the nonlocal Riemann–Liouville and Erdélyi–Kober q‐fractional integral conditions

Abstract

The solutions to fractional differential equations are a developing area of current research, given that these equations arise in various domains. In this article, we provide some necessary criteria for the existence, uniqueness, and different types of Ulam stability for a coupled implicit system requiring the conditions for nonlocal Riemann–Liouville and Erdélyi–Kober q‐fractional integral conditions. The uniqueness and existence results for the suggested coupled system are demonstrated using Banach fixed point theorem and Leray–Schauder of cone type. We also explore the various types of stability using classical methods of nonlinear functional analysis. To verify the effectiveness of our theoretical outcomes, we study an interesting example.