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This article investigates the issue of optimal control and approximate controllability results for fractional integrodifferential evolution equations with infinite delay of r ∈ (1, 2) in Banach space. In the beginning, we analyze approximate controllability results for fractional integrodifferential evolution equations using the fractional calculations, cosine families, and Banach fixed point theorem. After, we developed the continuous dependence of the fractional integrodifferential evolution equations by using the Henry-Gronwall inequality. Furthermore, we tested the existence of optimal controls for the Lagrange problem. Lastly, an application is presented to illustrate the theory of the main results.

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This work establishes the controllability of nondense fractional neutral delay differential equation under Hille-Yosida condition in Banach space. The outcomes are derived with the aid of fractional calculus theory, semigroup operator theory and Schauder fixed point theorem. Theoretical results are verified through illustration.

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