Non-existence for fractionally damped fractional differential problems
Classical Analysis and ODEs
2016-05-25 v1
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.
Keywords
Cite
@article{arxiv.1605.07432,
title = {Non-existence for fractionally damped fractional differential problems},
author = {Mohammed Kassim and Khaled M. Furati and Nasser-eddine Tatar},
journal= {arXiv preprint arXiv:1605.07432},
year = {2016}
}
Comments
in Acta Mathematica Scientia, vol 37, No. 1, 2017