Approximate Controllability of Fractional Stochastic Evolution Inclusions with Non-Local Conditions

Abstract

This article investigates the approximate controllability of non-linear fractional stochastic differential inclusions with non-local conditions. We establish a set of sufficient conditions for their approximate controllability and provide results in terms of controllability for the fractional stochastic control system. Our approach relies on using fractional calculus and the fixed-point theorem for multiple-valued operators. Finally, we present an illustrative example to support our findings.

On a New Stochastic Space of Solution for the Volterra-Type Summable Equations of Fuzzy Functions

“…(13) H F : the linear space of sequences of fuzzy functions. (14) [z]: the integral part of the real number z. (15) ℵ ≔ max 1, sup p w p 􏽮 􏽯.…”

“…Bakery and Mohammed [13] explained Kannan nonexpansive mappings on the variable exponent Cesàro sequence space of fuzzy functions. We can use the newly constructed stochastic space to explore more spaces of solutions for the fuzzy fractional evolution equations; see the following interesting articles: Abuasbeh et al [14], Niazi et al [15], and Iqbal et al's [16] studies. In this paper, geometric and topological properties are used to defne the space of fuzzy functions ((P qw F ) ς ) and the ideal space of its operators.…”