Nonexistence for fractional differential inequalities and systems in the sense of Erdelyi-Kober

Nonexistence theorems constitute an important part of the theory of differential and partial differential equations. Motivated by the numerous applications of fractional differential equations in diverse fields, in this paper, we studied sufficient conditions for the nonexistence of solutions (or, equivalently, necessary conditions for the existence of solutions) for nonlinear fractional differential inequalities and systems in the sense of Erdelyi-Kober. Our approach is based on nonlinear capacity estimates specifically adapted to the Erdelyi-Kober fractional operators and some integral inequalities.