GENERALIZED NONLOCAL BOUNDARY CONDITION FOR FRACTIONAL PANTOGRAPH DIFFERENTIAL EQUATION VIA HILFER FRACTIONAL DERIVATIVE

I. Ahmed; P. Kumam; J. Tariboon; A. Ibrahim; P.  Borisut; M. A.  Demba

Authors

I. Ahmed 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; Fixed Point Research Laboratory, Fixed Point Theory and Applications Research Group, Center of Excellence in Theoretical and Computational Science (TaCS-CoE), Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thung Khru, Bangkok 10140, Thailand; Department of Mathematics and Computer Science, Sule Lamido University, P.M.B 048 Kafin-Hausa, Jigawa State, Nigeria
P. Kumam 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; Fixed Point Research Laboratory, Fixed Point Theory and Applications Research Group, Center of Excellence in Theoretical and Computational Science (TaCS-CoE), Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thung Khru, Bangkok 10140, Thailand
J. Tariboon Nonlinear Dynamic Analysis Research Center, Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology, North Bangkok, Bangkok 10800,Thailand
A. Ibrahim School of Continuing Education, Bayero University Kano, P.M.B 3011 Kano, Nigeria
P. Borisut 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; Fixed Point Research Laboratory, Fixed Point Theory and Applications Research Group, Center of Excellence in Theoretical and Computational Science (TaCS-CoE), Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thung Khru, Bangkok 10140, Thailand
M. A. Demba 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; Fixed Point Research Laboratory, Fixed Point Theory and Applications Research Group, Center of Excellence in Theoretical and Computational Science (TaCS-CoE), Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thung Khru, Bangkok 10140, Thailand; Department of Mathematics, Faculty of Computing and mathematical Sciences, Kano University of Science and Technology, Wudil, P.M.B 3244 Kano State, Nigeria

Keywords:

Pantograph differential equation, Ulam stability, Fixed point theorems, Nonlocal condition, Hilfer-fractional derivative

Abstract

Fractional calculus has been very popular due to the application in real world problems. This paper aimed to investigate the existence, uniqueness and Ulam stability for nonlinear fractional pantograph differential equations with generalized nonlocal boundary conditions involving Hilfer fractional derivative. The analysis were done through Banach and Kranoselskii’s fixed point theorems. Finally, example are given to illustrate the theoretical results.