Blow-up of solutions to fractional differential inequalities involving ψ-Caputo fractional derivatives of different orders

Abstract

We consider a fractional differential inequality involving $ \psi $-Caputo fractional derivatives of different orders, with a polynomial nonlinearity and a singular potential term. Using the test function method and some integral inequalities, we establish nonexistence criteria of global solutions in both cases: $ \lim\limits_{t\to \infty}\psi(t)=\infty $ and $ \lim\limits_{t\to \infty}\psi(t)<\infty $.

Keywords

• fractional differential inequality
• global solution
• nonexistence
• ψ-caputo fractional derivative
• singular potential term