Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

Article

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Bull. Korean Math. Soc. 2018; 55(6): 1639-1657

Online first article November 7, 2018      Printed November 30, 2018

https://doi.org/10.4134/BKMS.b170887

Copyright © The Korean Mathematical Society.

Nonlocal boundary value problems for Hilfer fractional differential equations

Suphawat Asawasamrit, Atthapol Kijjathanakorn, Sotiris K. Ntouyas, Jessada Tariboon

King Mongkut's University of Technology, King Mongkut's University of Technology, King Abdulaziz University, King Mongkut's University of Technology

Abstract

In this paper, we initiate the study of boundary value problems involving Hilfer fractional derivatives. Several new existence and uniqueness results are obtained by using a variety of fixed point theorems. Examples illustrating our results are also presented.

Keywords: Hilfer fractional derivative, Riemann-Liouville fractional derivative, Caputo fractional derivative, boundary value problems, existence and uniqueness, fixed point theory

MSC numbers: 26A33, 34A08, 34B15