On solvability of pursuit and evasion problems for differential games with Hilfer fractional derivatives

Abstract

In this work, in a Banach space, we sovability the solvability of pursuit and evasion problems for differential games with Hilfer fractional derivatives of order $\alpha$, $0 < \alpha < 1$, of type $\mu$, $0 \leqslant \mu \leqslant 1$. Using Pontryagin first method and the theorem on strict separation, we prove two theorems on sufficient conditions for the solvability of pursuit and evasion problems on an interval. We solve one game problem describing the relaxation process in the glass formation of supercooled liquids.