A Coupled System of Nonlinear Langevin Fractional q- Difference Equations Associated with Two Different Fractional Orders in Banach Space

Abstract

In this research article, we study the coupled system of nonlinear Langevin fractional q-difference equations associated with two different fractional orders in Banach Space. The existence, uniqueness, and stability in the sense of Ulam are established for the proposed system. Our approach is based on the technique of measure of noncompactness combined with Mönch fixed point theorem, the implementation Banach contraction principle fixed point theorem, and the employment of Urs’s stability approach. Two examples illustrating the effectiveness of the theoretical results are presented.