An Extension of Caputo Fractional Derivative Operator by Use of Wiman’s Function

• Published in: Symmetry (Basel) Vol. 13; no. 12; p. 2238
• Main Authors: Goyal, Rahul, Agarwal, Praveen, Parmentier, Alexandra, Cesarano, Clemente
• Format: Journal Article
• Language: English
• Published: Basel MDPI AG 01-12-2021
• Subjects: beta function; classical Caputo fractional derivative operator; confluent hypergeometric function; Derivatives; Fractals; gamma function; Gauss hypergeometric function; Hypergeometric functions; Mellin transforms; Mittag–Leffler function; Operators (mathematics)
• ISSN: 2073-8994; 2073-8994
• DOI: 10.3390/sym13122238

The main aim of this work is to study an extension of the Caputo fractional derivative operator by use of the two-parameter Mittag–Leffler function given by Wiman. We have studied some generating relations, Mellin transforms and other relationships with extended hypergeometric functions in order to derive this extended operator. Due to symmetry in the family of special functions, it is easy to study their various properties with the extended fractional derivative operators.