Approximate Controllability and Optimal Control Analysis of Non‐Densely Defined Hilfer Fractional Stochastic Integro‐Differential Delay System With Hille–Yosida Operators Driven by Poisson Jumps

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The main motivation of our conversation is the approximate controllability and optimal control analysis for a non‐densely defined Hilfer fractional stochastic delay integro‐differential system with Poisson jumps. To do this, the principal findings are achieved by implementing the results of a multivalued map, fractional calculus, Hille–Yosida operators and fixed point approach of Bohnenblust and Karlin. We begin by discussing approximate controllability and then move on to neutral nonlocal conditions. Further, we extended the theory to the existence of optimal controls. Finally, a dedicated application has been developed to illustrate the theoretical and practical implications of primary findings.