Generalization of Special Functions and Explicit Form of Fractional Derivative of Rational Functions
Year: 2025
Type: article
Abstract: The goal of this paper is to extend the classical fractional derivatives. For this purpose, it is introduced the new extended modified Bessel function and also given an important relation between this new function I (q;x) and the confluent hypergeometric function 1F1( x). Besides, it is used to generalize the hypergeometric, the confluent hypergeometric and the extended beta functions by using the new extended modified Bessel function. Also, the asymptotic formulae and the generating function of the extended modified Bessel function are obtained. The extensions of classical fractional derivatives are defined via extended modifiedBessel function and, first time the fractional derivative of rational functions is explicitly given via complex partial fraction decomposition.
Authors: Ali Ozyapıcı, Yusuf Gurefe, Emine Mısırlı
Institutions: Cyprus International University, Usak University, Ege University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W4409953410