Non-existence for fractionally damped fractional differential problems. Issue 1 (January 2017)

• Record Type: Journal Article
• Authors: KASSIM, Mohammed D.; FURATI, Khaled M.; TATAR, Nasser-eddine
• Is Part Of: Acta mathematica scientia. Volume 37:Issue 1(2017)
• Page Start: 119
• Page End: 130
• Publication Date: 2017-01
• Subjects: nonexistence -- global solution -- fractional differential equation -- Riemann-Liouville fractional integral and fractional derivative; 26A33; Mathematical physics -- Periodicals; 530.15
• DOI: 10.1016/S0252-9602(16)30120-5
• Languages: English
• ISSNs: 0252-9602

Abstract

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.