Investigation of Ulam Stability Results of a Coupled System of Nonlinear Implicit Fractional Differential Equations

Zeeshan Ali, Poom Kumam, Kamal Shah and Akbar Zada
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Zeeshan Ali: Department of Mathematics, University of Peshawar, Peshawar, Khyber Pakhtunkhwa 25000, Pakistan
Poom Kumam: Center of Excellence in Theoretical and Computational Science (TaCS-CoE) & KMUTTFixed Point Research Laboratory, Room SCL 802 Fixed Point Laboratory, Science Laboratory Building, Departments of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, Thailand
Kamal Shah: Department of Mathematics, University of Malakand, Dir(L), Khyber Pakhtunkhwa 18800, Pakistan
Akbar Zada: Department of Mathematics, University of Peshawar, Peshawar, Khyber Pakhtunkhwa 25000, Pakistan

Mathematics, 2019, vol. 7, issue 4, 1-26

Abstract: This manuscript deals with the existence theory, uniqueness, and various kinds of Ulam–Hyers stability of solutions for a class and coupled system of fractional order differential equations involving Caputo derivatives. Applying Schaefer and Banach’s fixed point approaches, existence and uniqueness results are obtained for the proposed problems. Stability results are investigated by using the classical technique of nonlinear functional analysis. Examples are given with each problem to illustrate the main results.

Keywords: Caputo fractional derivative; implicit differential equation; Green’s function; implicit coupled system; existence theory; Ulam stability (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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