On the absence of global solutions to two-times-fractional differential inequalities involving Hadamard-Caputo and Caputo fractional derivatives

Abstract

In this paper, we consider a two-times nonlinear fractional differential inequality involving both Hadamard-Caputo and Caputo fractional derivatives of different orders, with a singular potential term. We obtain sufficient criteria depending on the parameters of the problem, for which a global solution does not exist. Some examples are provided to support our main results.

Keywords

• two-times fractional differential inequality
• global solution
• nonexistence
• hadamard-caputo fractional derivative
• caputo fractional derivative