Related papers: Katugampola Fractional Calculus With Generalized $…
In this paper, the generalized fractional integral operators of two generalized Mittag-Leffler type functions are investigated. The special cases of interest involve the generalized Fox--Wright function and the generalized M-series and…
The subject of this note is the mixed Katugampola fractional integral of a bivariate function defined on a rectangular region in the Cartesian plane. This is a natural extension of the Katugampola fractional integral of a univariate…
The main objective of this paper is to obtain generalization of some Gruss-type inequalities in case of functional bounds by using a generalized Katugampola fractional integral.
In this paper we obtain a generalization of some integral inequalities related to Chebyshev`s functional by using a generalized Katugampola fractional integral.
In this paper, certain generalized fractional derivative formulae are introduced involving the k-Mittag-Leffler function. Then their image formulae (using Beta transform, Laplace transform and Whittaker transform) are also established. The…
The objective of this paper is to present an approximation formula for the Katugampola fractional integral, that allows us to solve fractional problems with dependence on this type of fractional operator. The formula only depends on…
The existence and stability results for a class of fractional differential equations involving generalized Katugampola derivative are presented herein. Some fixed point theorems are used and enlightening examples of obtained result are also…
The following material was created with the idea of being used for an introductory fractional calculus course. A recapitulation of the history of fractional calculus is presented, as well as the different attempts at fractional derivatives…
Generalized integral formulas involving the generalized modified k-Bessel function $J_{k,\nu }^{c,\gamma ,\lambda }\left( z\right) $ of first kind are expressed in terms generalized $k-$Wright functions. Some interesting special cases of…
In this study the general formula for differential and integral operations of fractional calculus via fractal operators by the method of cumulative diminution and cumulative growth is obtained. The under lying mechanism in the success of…
In this manuscript, we generalize F-calculus to apply it on fractal Tartan spaces. The generalized standard F-calculus is used to obtain the integral and derivative of the functions on the fractal Tartan with different dimensions. The…
We aim to introduce the generalized multiindex Bessel function $J_{\left( \beta _{j}\right) _{m},\kappa ,b}^{\left( \alpha _{j}\right)_{m},\gamma ,c}\left[ z\right] $ and to present some formulas of the Riemann-Liouville fractional…
In this paper, the generalized fractional operators involving Appell's function $F_3$ in the kernel due to Marichev-Saigo-Maeda are applied to the generalized $K$-Wright function. These fractional operators when applied to power multipliers…
In this tutorial survey we recall the basic properties of the special function of the Mittag-Leffler and Wright type that are known to be relevant in processes dealt with the fractional calculus. We outline the major applications of these…
This paper presents the fractional trigonometric functions in complex-valued space and proposes a short outline of local fractional calculus of complex function in fractal spaces.
This short study consists of two parts, firstly we obtain some inequalities on Caputo Fractional derivatives using the elementary inequalities. Secondly we establish several new inequalities including Caputo fractional derivatives for…
In this present paper our aim is to deal with two integral transforms which involving the Gauss hypergeometric function as its kernels. We prove some compositions formulas for such a generalized fractional integrals with k Bessel function.…
In this work we show that it is possible to calculate the fractional integrals and derivatives of order $\alpha$ (using the Riemann-Liouville formulation) of power functions $\left( t-\ast\right) ^{\beta}$ with $\beta$ being any real value,…
We give a unified interpretation of confluences, contiguity relations and Katz's middle convolutions for linear ordinary differential equations with polynomial coefficients and their generalization to partial differential equations. The…
Many possible definitions have been proposed for fractional derivatives and integrals, starting from the classical Riemann-Liouville formula and its generalisations and modifying it by replacing the power function kernel with other kernel…