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.

<abstract><p>In this study, we investigate differential and integral equations of some hybrid families of truncated exponential-based Sheffer polynomials. We also derive some integro-differential equation and new recurrence relations for the truncated exponential based Sheffer polynomials by using the factorization method. We also discuss some special cases as illustrative examples.</p></abstract>