Controabillity of stochastic pantograph differential inclusions with Hilfer fractional derivative

Abstract

This work aims to investigates the controllability of a class
of fractional stochastic pantograph inclusions with Hilfer
fractional derivative (HFD). The controllability results
are obtained by using fractional calculus theory,
semigroup theory, stochastic analysis, and nonlinear
alternative for contractive maps under sufficient conditions.
An example is given to validate the results.