Non-existence for fractionally damped fractional differential problems. Issue 1 (January 2017) - KASSIM, Mohammed D.; FURATI, Khaled M.; TATAR, Nasser-eddine
Abstract: In this paper, we are concerned with a fractional differential inequality containing a lower order fractional derivative and a polynomial source term in the right hand side. A non-existence of non-trivial global solutions result is proved in an appropriate space by means of the test-function method. The range of blow up is found to depend only on the lower order derivative. This is in line with the well-known fact for an internally weakly damped wave equation that solutions will converge to solutions of the parabolic part.