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In this paper, we explain the approximate controllability of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="sans-serif">Ψ</mi></semantics></math></inline-formula>-Hilfer fractional neutral differential equations with infinite delay. The outcome is demonstrated using the infinitesimal operator, fractional calculus, semigroup theory, and the Krasnoselskii’s fixed point theorem. To begin, we emphasise the presence of the mild solution and show that the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="sans-serif">Ψ</mi></semantics></math></inline-formula>-Hilfer fractional system is approximately controllable. Additionally, we present theoretical and practical examples.