On generalized $\mathtt{k}$-fractional derivative operator
Gauhar Rahman, Shahid Mubeen, Kottakkaran Sooppy Nisar
Abstract
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.
Topics & Concepts
Operator (biology)Hypergeometric functionMathematicsFractional calculusDerivative (finance)Hypergeometric distributionMellin transformPure mathematicsCombinatoricsMathematical physicsMathematical analysisFourier transformGeneTranscription factorBiochemistryChemistryFinancial economicsEconomicsRepressorFractional Differential Equations SolutionsMathematical functions and polynomialsIterative Methods for Nonlinear Equations