School of Mathematics and Statistics
University of Glasgow
Glasgow G12 8SQ, UK
email: jeffrey.webb@glasgow.ac.uk
Jeffrey R. L. Webb
Abstract:
We prove nonexistence of global solution of fractional differential inequalities of the form
\(D^{\alpha}u(t) \ge \lambda t^{\beta}|u(t)|^{p}\) when \(p>1\) for each of the Riemann-Liouville and Caputo fractional derivatives. This is motivated by work of Laskri and Tatar (Comput. Math.\Appl. (2010)) and
Shan and Lv (Filomat (2024)). The result of Laskri-Tatar was claimed to be false by Zhang, Liu, Wu and Cui (J. Funct. Spaces (2017)) with a correction and counter-example. We show that the counter-example and the claims are not accurate. We use a different method to that of Laskri and Tatar, our result supports the one of Laskri and Tatar. We also improve on the result in Shan and Lv paper by considering a more general problem and giving a more precise conclusion.
Submitted March 25, 2024. Published July 30, 2024.
Math Subject Classifications: 34A08, 34A40, 45D05.
Key Words: Fractional differential equations; non-existence; Volterra integral equation.
DOI: 10.58997/ejde.2024.40w
Show me the PDF file (373 KB), TEX file for this article.
|
Jeffrey R. L. Webb School of Mathematics and Statistics University of Glasgow Glasgow G12 8SQ, UK email: jeffrey.webb@glasgow.ac.uk |
|---|
Return to the EJDE web page