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The kηHyperbolic Functions
(Hikari Ltd,, 2016)The main objetive of this paper is to present and discuss a family of functions dependent on ve parameters that generalize the one introduced by A. Ungar [8]. The action of RiemannLiouville fractional operators over them ... 
The kFractional Logistic Equation with kCaputo Derivative
(Hikari Ltd, 2015)A generalization of the fractional logistic equation by using kCaputo derivative is introduced. Also a solution that can be expressed en terms of the kMittagLe er function is obtained. The development of this paper ... 
On the pkMittagLeffler Function
(Hikari Ltd, 2017)In this paper, we define the function pE γ k,α,β(z), estudy its analytic properties, some elementary properties as its integral expression, its relationship with the fractional operator of RiemannLiouville and investigate ... 
The Generalized kαMillerRoss Function
(Hikari Ltd, 2016) 
The Mittag–Leffler function and its application to the ultrahyperbolic timefractional diffusionwave equation
(Taylor & Francis Group, 201603)In this paper we study an ndimensional generalization of timefractional diffusionwave equation, where the Laplacian operator is replaced by the ultrahyperbolic operator and the timefractional derivative is taken in the ... 
An The New RiemannLiouville Fractional Operator Extended
(JS Publication, 2017)In this paper we will introduce a new and modi ed RiemannLiouville fractional operator that resulted from modifying the extended fractional derivative due to M. Ozarslan. We will study some familiar functions regarding ... 
kFractional Trigonometric Functions
(Hikari Ltd, 2014)Based on the kMittagLefler function and the k Exponential Function we introduce families of functions that allows us define new fractional trigonometric functions that contain the classical trigonometric functions ... 
A generalization of the kinetic equation using the prabhakartype operators
(Honam Mathematical Society, 2017)Fractional kinetic equations are investigated in order to describe the various phenomena governed by anomalous reaction in dynamical systems with chaotic motion. Many authors have pro vided solutions of various families ... 
An New Extended Beta Function
(JS Publication, 2017)In this paper, we will present a new and modi ed extended classical Gamma, Beta functions. Some properties basic are studied, such as the integral representations, functional relations and we will evaluate the action of ... 
An Alternative De nition for the kRiemannLiouville Fractional Derivative
(HIKARI Ltd, 2015)The aim of this paper is to introduce an alternative de nition for the kRiemannLiouville fractional derivative given in [6] and whose advantage is that it is the left inverse of the corresponding of kRiemannLiouville ...