Next Article in Journal
Some Identities Involving Certain Hardy Sums and General Kloosterman Sums
Previous Article in Journal
SE-IYOLOV3: An Accurate Small Scale Face Detector for Outdoor Security
Previous Article in Special Issue
Absence of Global Solutions for a Fractional in Time and Space Shallow-Water System
Open AccessArticle

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

1
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
2
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
3
Department of Mathematics and Computer Science, Sule Lamido University, Kafin-Hausa, Jigawa State P.M.B 048, Nigeria
4
Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan
5
Department of Mathematics, University of Malakand, Chakadara Dir(L), Khyber Pakhtunkhwa 18800, Pakistan
6
Department of Mathematics and Basic Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia
7
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
8
Department of Mathematics, Faculty of Computing and Mathematical Sciences, Kano University of Science and Technology, Wudil, Kano State P.M.B 3244, Nigeria
*
Author to whom correspondence should be addressed.
Mathematics 2020, 8(1), 94; https://doi.org/10.3390/math8010094
Received: 27 November 2019 / Revised: 12 December 2019 / Accepted: 18 December 2019 / Published: 7 January 2020
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. View Full-Text
Keywords: Hilfer fractional derivative; Ulam stability; pantograph differential equation; nonlocal integral condition Hilfer fractional derivative; Ulam stability; pantograph differential equation; nonlocal integral condition
MDPI and ACS Style

Ahmed, I.; Kumam, P.; Shah, K.; Borisut, P.; Sitthithakerngkiet, K.; Ahmed Demba, M. Stability Results for Implicit Fractional Pantograph Differential Equations via ϕ-Hilfer Fractional Derivative with a Nonlocal Riemann-Liouville Fractional Integral Condition. Mathematics 2020, 8, 94.

Show more citation formats Show less citations formats
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map by Country/Region

1
Back to TopTop