Electron. J. Differential Equations, Vol. 2018 (2018), No. 87, pp. 1-16.

Multi-term fractional-order boundary-value problems with nonlocal integral boundary conditions

Ahmed Alsaedi, Najla Alghamdi, Ravi P. Agarwal, Sotiris K. Ntouyas, Bashir Ahmad

Abstract:
In this article, we introduce a class of multi-term fractional-order boundary-value problems involving nonlocal integral boundary conditions. Existence results for the given problem are obtained by means of standard tools of fixed point theory. The results are illustrated with the aid of examples and make a useful contribution to the existing literature on the topic.

Submitted February 25, 2018. Published April 10, 2018.
Math Subject Classifications: 34A08, 34B10.
Key Words: Caputo fractional derivative; integral boundary condition; multi-term fractional differential equations; existence; fixed point.

An addendum was posted on May 2, 2018. It indicates that the converse part of Lemma 2.4 is incorrect. See the last page of this article.

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Ahmed Alsaedi
Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group
Department of Mathematics, Faculty of Science
King Abdulaziz University
P.O. Box 80203, Jeddah 21589, Saudi Arabia
email: aalsaedi@hotmail.com
  Najla Alghamdi
Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group
Department of Mathematics, Faculty of Science
King Abdulaziz University
P.O. Box 80203, Jeddah 21589, Saudi Arabia
email: njl-ghamdi@hotmail.com
Ravi P. Agarwal
Department of Mathematics
Texas A&M University
Kingsville, TX 78363-8202, USA
email: Ravi.Agarwal@tamuk.edu
Sotiris K. Ntouyas
Department of Mathematics
University of Ioannina
451 10 Ioannina, Greece
email: sntouyas@uoi.gr
Bashir Ahmad
Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group
Department of Mathematics, Faculty of Science
King Abdulaziz University
P.O. Box 80203, Jeddah 21589, Saudi Arabia
email: bashirahmad_qau@yahoo.com

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