Non-existence for fractionally damped fractional differential problems

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• 作者：Mohammed D. KASSIM ; ^{dahan@kfupm.edu.sa} ; Khaled M. FURATI ^{kmfurati@kfupm.edu.sa} ; Nasser-eddine TATAR ^{tatarn@kfupm.edu.sa}
• 关键词：nonexistence ; global solution ; fractional differential equation ; Riemann-Liouville fractional integral and fractional derivative
• 刊名：Acta Mathematica Scientia
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：37
• 期：1
• 页码：119-130
• 全文大小：191 K
• 卷排序：37

文摘

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.