Nonexistence results for fractional differential inequalities

We prove nonexistence of global solution of fractional differential inequalities of the form \(Dαu(t) ≥ {λ}tβ|u(t)|ᵖ\) 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. For more information see https://ejde.math.txstate.edu/Volumes/2024/40/abstr.html