A Mathematical Theoretical Study of a Coupled Fully Hybrid (k, Φ)-Fractional Order System of BVPs in Generalized Banach Spaces

Abstract

In this paper, we study a coupled fully hybrid system of (k,Φ)–Hilfer fractional differential equations equipped with non-symmetric (k,Φ)–Riemann-Liouville (RL) integral conditions. To prove the existence and uniqueness results, we use the Krasnoselskii and Perov fixed-point theorems with Lipschitzian matrix in the context of a generalized Banach space (GBS). Moreover, the Ulam–Hyers (UH) stability of the solutions is discussed by using the Urs’s method. Finally, an illustrated example is given to confirm the validity of our results.

Topology degree results on a G-ABC implicit fractional differential equation under three-point boundary conditions

“…This type of derivative is commonly used in fractional calculus with various operators to describe complex systems with non-integer order dynamics. In fact, by taking this fractional derivative, the researchers can better model the behavior of these systems and gain a deeper understanding of their underlying dynamics, see for example [ 22 – 24 ] and references cited therein.…”