A Study of the $\ell$-Extension to the Results of Classical Calculus

Abstract

In this paper, new generalizations of the hyper Bessel type differential operator called it as $\ell$-H derivative operator, are studied, and using these, some of the classical results of calculus are extended. Also, new generalization of a natural number is defined and then its combinatorial properties are extended. After this, the $\ell$-H integral is defined, and then its basic properties are assessed and classical results of calculus pertaining to the integral are extended.