2017/03/01 by Ali Özyapıcı, Ozyapici, Ali, Yusuf Gürefe +3
Mathematics · #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Fractional Differential Equations Solutions #Iterative Methods for Nonlinear Equations #Mathematical functions and polynomials
paper · pdf · doi:10.48550/arxiv.1703.01903
openalex publication_date 2017/03/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The goal of this paper is to extend the classical and multiplicative 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(v,q;x) and the confluent hypergeometric function. 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 and multiplicative fractional derivatives are defined via extended modified Bessel function and, first time the fractional derivative of rational functions is explicitly given via complex partial fraction decomposition.