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Mathematics 2019, 7(4), 341; https://doi.org/10.3390/math7040341

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

1
Department of Mathematics, University of Peshawar, Peshawar, Khyber Pakhtunkhwa 25000, Pakistan
2
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
3
Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan
4
Department of Mathematics, University of Malakand, Dir(L), Khyber Pakhtunkhwa 18800, Pakistan
*
Author to whom correspondence should be addressed.
Received: 18 February 2019 / Revised: 24 March 2019 / Accepted: 28 March 2019 / Published: 9 April 2019
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PDF [524 KB, uploaded 24 April 2019]

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. View Full-Text
Keywords: Caputo fractional derivative; implicit differential equation; Green’s function; implicit coupled system; existence theory; Ulam stability Caputo fractional derivative; implicit differential equation; Green’s function; implicit coupled system; existence theory; Ulam stability
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Ali, Z.; Kumam, P.; Shah, K.; Zada, A. Investigation of Ulam Stability Results of a Coupled System of Nonlinear Implicit Fractional Differential Equations. Mathematics 2019, 7, 341.

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