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

Symmetry

Praveen Agarwal¹  Rahul Goyal¹  Alexandra Parmentier²  Clemente Cesarano³ 

[1] Department of Mathematics, Anand International College of Engineering, Jaipur 303012, India;National Institute of Astrophysics—IAPS, 00133 Rome, Italy;Section of Mathematics, International Telematic University Uninettuno, 00186 Rome, Italy;

关键词: classical Caputo fractional derivative operator;    beta function;    gamma function;    Gauss hypergeometric function;    confluent hypergeometric function;    Mittag–Leffler function;   

DOI  :  10.3390/sym13122238

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown