Abstract
In this paper, we study the non-existence of non-trivial global solutions for a fractional differential inequality containing a lower order fractional derivative and a polynomial source term on the right hand side. Non-existence of non-trivial global solutions result is proved in an appropriate space by means of the test-function method. The range of values of the exponent involved there (ensuring non-existence) is found to depend only on the lower order derivative. This is in agreement with the integer order case. Numerical examples are given to illustrate the results. (C) 2016 Elsevier B.V. All rights reserved.