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arXiv · 1605.07432

Non-existence for fractionally damped fractional differential problems

Mohammed Kassim·Khaled M. Furati·Nasser-eddine Tatar
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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.

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Mohammed Kassim, Khaled M. Furati, Nasser-eddine Tatar. 2016-05-24. Non-existence for fractionally damped fractional differential problems. https://arxiv.org/abs/1605.07432

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