ﻻ يوجد ملخص باللغة العربية
The main objective of this article is to present $ u$-fractional derivative $mu$-differentiable functions by considering 4-parameters extended Mittag-Leffler function (MLF). We investigate that the new $ u$-fractional derivative satisfies various properties of order calculus such as chain rule, product rule, Rolles and mean-value theorems for $mu$-differentiable function and its extension. Moreover, we define the generalized form of inverse property and the fundamental theorem of calculus and the mean-value theorem for integrals. Also, we establish a relationship with fractional integral through truncated $ u$-fractional integral.
In this study our aim to define the extended $(p,q)$-Mittag-Leffler(ML) function by using extension of beta functions and to obtain the integral representation of new function. We also take the Mellin transform of this new function in terms of Wright
We establish a new formula for the fractional derivative with Mittag-Leffler kernel, in the form of a series of Riemann-Liouville fractional integrals, which brings out more clearly the non-locality of fractional derivatives and is easier to handle f
In this paper, we present an extension of Mittag-Leffler function by using the extension of beta functions ({O}zergin et al. in J. Comput. Appl. Math. 235 (2011), 4601-4610) and obtain some integral representation of this newly defined function. Also
This paper deals with a Euler type integral operator involving k-Mittag-Leffler function defined by Gupta and Parihar [8]. Furthermore, some special cases are also taken into consideration.
We consider an integral transform introduced by Prabhakar, involving generalised multi-parameter Mittag-Leffler functions, which can be used to introduce and investigate several different models of fractional calculus. We derive a new series expressi