Eur. Phys. J. Special Topics 226, 3513–3524 (2017)
https://doi.org/10.1140/epjst/e2018-71007-2

Regular Article

Nonexistence of global solutions for a class of sequential fractional differential inequalities

Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia

^a e-mail: bsamet@ksu.edu.sa

Received: 16 April 2017
Received in final form: 3 August 2017
Published online: 25 July 2018

Abstract

We provide sufficient conditions for the non-existence of global solutions for a certain class of sequential fractional differential inequalities involving Riemann-Liouville left-sided fractional derivatives with different orders. To the best of our knowledge, the study of non-existence of solutions for fractional differential problems with sequential fractional derivatives has not been investigated until now. Our approach is based on the test function method.