Research article

On generalized $\mathtt{k}$-fractional derivative operator

  • Received: 11 November 2019 Accepted: 03 February 2020 Published: 19 February 2020
  • MSC : 33C05, 33C15

  • The principal aim of this paper is to introduce $\mathtt{k}$-fractional derivative operator by using the definition of $\mathtt{k}$-beta function. This paper establishes some results related to the newly defined fractional operator such as the Mellin transform and the relations to $\mathtt{k}$-hypergeometric and $\mathtt{k}$-Appell's functions. Also, we investigate the $\mathtt{k}$-fractional derivative of $\mathtt{k}$-Mittag-Leffler and the Wright hypergeometric functions.

    Citation: Gauhar Rahman, Shahid Mubeen, Kottakkaran Sooppy Nisar. On generalized $\mathtt{k}$-fractional derivative operator[J]. AIMS Mathematics, 2020, 5(3): 1936-1945. doi: 10.3934/math.2020129

    Related Papers:

  • The principal aim of this paper is to introduce $\mathtt{k}$-fractional derivative operator by using the definition of $\mathtt{k}$-beta function. This paper establishes some results related to the newly defined fractional operator such as the Mellin transform and the relations to $\mathtt{k}$-hypergeometric and $\mathtt{k}$-Appell's functions. Also, we investigate the $\mathtt{k}$-fractional derivative of $\mathtt{k}$-Mittag-Leffler and the Wright hypergeometric functions.


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