数学物理学报(英文版) ›› 2017, Vol. 37 ›› Issue (1): 119-130.doi: 10.1016/S0252-9602(16)30120-5

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NON-EXISTENCE FOR FRACTIONALLY DAMPED FRACTIONAL DIFFERENTIAL PROBLEMS

Mohammed D. KASSIM, Khaled M. FURATI, Nasser-eddine TATAR   

  1. Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran, 31261, Saudi Arabia
  • 收稿日期:2015-10-18 修回日期:2016-04-18 出版日期:2017-02-25 发布日期:2017-02-25
  • 通讯作者: Mohammed D. KASSIM,E-mail:dahan@kfupm.edu.sa E-mail:dahan@kfupm.edu.sa
  • 作者简介:Khaled M. FURATI,E-mail:kmfurati@kfupm.edu.sa;Nasser-eddine TATAR,E-mail:tatarn@kfupm.edu.sa

NON-EXISTENCE FOR FRACTIONALLY DAMPED FRACTIONAL DIFFERENTIAL PROBLEMS

Mohammed D. KASSIM, Khaled M. FURATI, Nasser-eddine TATAR   

  1. Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran, 31261, Saudi Arabia
  • Received:2015-10-18 Revised:2016-04-18 Online:2017-02-25 Published:2017-02-25
  • Contact: Mohammed D. KASSIM,E-mail:dahan@kfupm.edu.sa E-mail:dahan@kfupm.edu.sa
  • About author:Khaled M. FURATI,E-mail:kmfurati@kfupm.edu.sa;Nasser-eddine TATAR,E-mail:tatarn@kfupm.edu.sa

摘要:

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.

关键词: nonexistence, global solution, fractional differential equation, Riemann-Liouville fractional integral and fractional derivative

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.

Key words: nonexistence, global solution, fractional differential equation, Riemann-Liouville fractional integral and fractional derivative