This paper addresses the approximate controllability results for Hilfer fractional stochastic differential inclusions of order $1<\mathsf{q}<2$. Stochastic analysis, cosine families, fixed point theory, and fractional calculus provide the foundation of the main results. First, we explored the prospects of finding mild solutions for the Hilfer fractional stochastic differential equation. Subsequently, we determined that the specified system is approximately controllable. Finally, an example displays the theoretical application of the results.

By practicing the manner of semigroup theory and Banach contraction theorem, the existence and uniqueness of mild and classical solutions of nonlinear integrodifferential equations with time varying delay in Banach spaces is showed. Certainly, an example is revealed to justify the abstract idea. By practicing the manner of semigroup theory and Banach contraction theorem, the existence and uniqueness of mild and classical solutions of nonlinear integrodifferential equations with time varying delay in Banach spaces is showed. Certainly, an example is revealed to justify the abstract idea.