Existence and uniqueness for a coupled system of fractional equations involving Riemann-Liouville and Caputo derivatives with coupled Riemann-Stieltjes integro-multipoint boundary conditions

Abstract

<abstract><p>Recently, coupled systems of fractional differential equations play a central role in the modelling of many systems in e.g., financial economics, ecology, and many more. This study investigates the existence and uniqueness of solutions for a nonlinear coupled system of fractional differential equations involving Riemann-Liouville and Caputo derivatives with coupled Riemann-Stieltjes integro-multipoint boundary conditions. The main tools are known fixed point theorems, namely, Leray-Schauder alternative, Banach fixed point theorem, and the Krasnoselskii fixed point theorem. The new system, which can be considered as a generalized version of many previous fascinating systems, is where the article's novelty lies. Examples are presented to illustrate the results. In this way, we generalize several earlier results.</p></abstract>

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“…Fixed-point theorems have recently played a vital role in proving many interesting results (see, e.g., [39][40][41]).…”

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“…These ideas have recently been used as the foundation for breaking down numerous mathematical problems. See, for instance [2,15,36] and the references contained therein. For more sophisticated applications of dynamical systems studied using fractional calculus, we refer to [4,14,24,33].…”