Nonexistence results of Caputo-type fractional problem

Abstract

Abstract In this paper, we deal with Caputo-type fractional differential inequality where there is a low-order fractional derivative with the term polynomial source. We investigate the nonexistence of nontrivial global solutions in a suitable space via the test function technique and some properties of fractional integrals. Finally, we demonstrate three examples to illustrate our results. The presented results are more general than those in the literature, which can be obtained as particular cases.

Keywords

• Nonexistence
• Caputo fractional derivative
• Global solution
• Test function method