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 King Mongkut's University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, Thailand
P. Kumam King Mongkut's University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, Thailand
J. Tariboon 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 King Mongkut's University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, Thailand
M. A. Demba University of Science and Technology, Wudil, P.M.B 3244 Kano State, Nigeria

Keywords:

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

Abstract

Fractional calculus has been very popular due to its 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 was done through Banach and Kranoselskii's fixed point theorems. Finally, examples are given to illustrate the theoretical results.