NON-EXISTENCE FOR FRACTIONALLY DAMPED FRACTIONAL DIFFERENTIAL PROBLEMS

doi:10.1016/S0252-9602(16)30120-5

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.

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

Mohammed D. KASSIM, Khaled M. FURATI, Nasser-eddine TATAR. NON-EXISTENCE FOR FRACTIONALLY DAMPED FRACTIONAL DIFFERENTIAL PROBLEMS[J].Acta mathematica scientia,Series B, 2017, 37(1): 119-130.

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