On a System of ψ -Caputo Hybrid Fractional Differential Equations with Dirichlet Boundary Conditions

Muath Awadalla, Kinda Abuasbeh, Muthaiah Subramanian and Murugesan Manigandan
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Muath Awadalla: Department of Mathematics and Statistics, College of Science, King Faisal University, Al Ahsa 31982, Saudi Arabia
Kinda Abuasbeh: Department of Mathematics and Statistics, College of Science, King Faisal University, Al Ahsa 31982, Saudi Arabia
Muthaiah Subramanian: Department of Mathematics, KPR Institute of Engineering and Technology, Coimbatore 641020, India
Murugesan Manigandan: Department of Mathematics, Sri Ramakrishna Mission Vidyalaya College of Arts and Science, Coimbatore 641020, India

Mathematics, 2022, vol. 10, issue 10, 1-15

Abstract: In this article, we investigate sufficient conditions for the existence and stability of solutions to a coupled system of ψ -Caputo hybrid fractional derivatives of order 1 < υ ≤ 2 subjected to Dirichlet boundary conditions. We discuss the existence and uniqueness of solutions with the assistance of the Leray–Schauder alternative theorem and Banach’s contraction principle. In addition, by using some mathematical techniques, we examine the stability results of Ulam–Hyers. Finally, we provide one example in order to show the validity of our results.

Keywords: ? -Caputo fractional derivative; existence; fixed point theorems; Ulam–Hyers stability (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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