On Global Solutions to a ψ-Caputo Fractional Inequality

This paper investigates the absence of globally defined, non-trivial solutions for some fractional differential inequalities of the ψ-Caputo type, with polynomial sources involving fractional derivatives. We rigorously establish these results within an appropriate function space using properties of ψ-fractional integrals and derivatives and the test function technique. To demonstrate the applicability and enhance understanding, we provide three illustrative examples. Our findings broaden the scope of previous literature, encompassing existing results as special cases.