Results on approximate controllability of fractional stochastic Sobolev‐type Volterra–Fredholm integro‐differential equation of order 1 &lt; <i>r</i> &lt; 2

Abstract

The main motivation of our conversation is the approximate controllability of fractional stochastic Sobolev‐type Volterra–Fredholm integro‐differential equation of order 1 &lt; r &lt; 2. Using principles and ideas from stochastic analysis, the theory of cosine family, fractional calculus, and Banach fixed point techniques, the key findings are established. We begin by emphasizing the existence of mild solutions and then demonstrate the approximate controllability of the fractional stochastic control equation. We then apply our findings to the theory of nonlocal conditions. At last, an application is established for drawing the theory of the main results.

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