The main objective of this paper is to establish the extension of an extended fractional derivative operator by using an extended beta function recently defined by Parmar et al. by considering the Bessel functions in its kernel. We also give some results related to the newly defined fractional operator, such as Mellin transform and relations to extended hypergeometric and Appell's function via generating functions.
M. Bohner et al., "A Further Extension of the Extended Riemann-Liouville Fractional Derivative Operator," Turkish Journal of Mathematics, vol. 42, no. 5, pp. 2631-2642, TUBITAK, Sep 2018.
The definitive version is available at https://doi.org/10.3906/mat-1805-139
Mathematics and Statistics
Keywords and Phrases
Appell's function; Extended hypergeometric function; Fractional derivative; Hypergeometric function; Mellin transform
International Standard Serial Number (ISSN)
Article - Journal
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01 Sep 2018