Stability Results for Implicit Fractional Pantograph Differential Equations via ? -Hilfer Fractional Derivative with a Nonlocal Riemann-Liouville Fractional Integral Condition

Idris Ahmed, Poom Kumam, Kamal Shah, Piyachat Borisut, Kanokwan Sitthithakerngkiet and Musa Ahmed Demba
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Idris Ahmed: KMUTTFixed Point Research Laboratory, Room SCL 802 Fixed Point Laboratory, Science Laboratory Building, Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, Thailand
Poom Kumam: Center of Excellence in Theoretical and Computational Science (TaCS-CoE), Science Laboratory Building, 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, Chakadara Dir(L), Khyber Pakhtunkhwa 18800, Pakistan
Piyachat Borisut: KMUTTFixed Point Research Laboratory, Room SCL 802 Fixed Point Laboratory, Science Laboratory Building, Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, Thailand
Kanokwan Sitthithakerngkiet: Intelligent and Nonlinear Dynamic Innovations Research Center, Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok (KMUTNB), Wongsawang, Bangsue, Bangkok 10800, Thailand
Musa Ahmed Demba: KMUTTFixed Point Research Laboratory, Room SCL 802 Fixed Point Laboratory, Science Laboratory Building, Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, Thailand

Mathematics, 2020, vol. 8, issue 1, 1-21

Abstract: This paper presents a class of implicit pantograph fractional differential equation with more general Riemann-Liouville fractional integral condition. A certain class of generalized fractional derivative is used to set the problem. The existence and uniqueness of the problem is obtained using Schaefer’s and Banach fixed point theorems. In addition, the Ulam-Hyers and generalized Ulam-Hyers stability of the problem are established. Finally, some examples are given to illustrative the results.

Keywords: Hilfer fractional derivative; Ulam stability; pantograph differential equation; nonlocal integral condition (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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