NON-EXISTENCE FOR FRACTIONALLY DAMPED FRACTIONAL DIFFERENTIAL PROBLEMS

• Published in: Acta mathematica scientia Vol. 37; no. 1; pp. 119 - 130
• Main Author: Mohnmmed D, KASSIM Khaled M. FURATI Nasser-eddine TATAR
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 2017; Department of Mathematics and Statistics,King Fahd University of Petroleum and Minerals,Dhahran,31261,Saudi Arabia
• Subjects: 26A33; fractional differential equation; global solution; nonexistence; Riemann-Liouville fractional integral and fractional derivative; 函数法; 分数导数; 分数阶; 多项式; 微分不等式; 微分问题; 解的存在性; 阻尼波动方程; fractional differential equation; nonexistence; global solution; 26A33; Riemann-Liouville fractional integral and fractional derivative
• ISSN: 0252-9602; 1572-9087
• DOI: 10.1016/S0252-9602(16)30120-5

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.