نتایج جستجو برای: leffler

تعداد نتایج: 1008  

2014
Vijay Kumar Singhal

The present paper aims at the study and derivation of Saigo generalized fractional integral operator involving product of Hfunction of one variable and general class of polynomials. On account of the most general nature of the operator, H-function and general class of polynomials occurring in the main result, a large number of known and new results involving Rieman-Liouville, ErdélyiKober Fract...

2018
Arran Fernandez Dumitru Baleanu

*Correspondence: [email protected] 1Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, UK Full list of author information is available at the end of the article Abstract We establish analogues of the mean value theorem and Taylor’s theorem for fractional differential operators defined using a Mittag–Leffler kernel. We formulate a new model for the fract...

2008
N. M. Grahovac M. M. Žigić

This paper deals with a new mathematical model of the hamstring muscle group. The proposed viscoelastic model includes fractional derivatives of stretching force and elongation as well as restrictions on the coefficients that follow from the second law of thermodynamics. On the basis of experimental data four coefficients of the model have been calculated by numerical procedure. Obtained result...

2006
V. V. NOVIKOV K. W. WOJCIECHOWSKI O. A. KOMKOVA T. THIEL

It has been shown that anomalous relaxation in dielectrics can be described in terms of equations with fractional derivatives. The solutions of the resulting equation with fractional derivatives are expressed by the Mittag –Leffler function and the Fox function. The conditions of a change from the Debye relaxation to “slow” (anomalous) relaxation with a power time dependence have been examined ...

Journal: :Automatica 2009
Yan Li Yangquan Chen Igor Podlubny

In this paper we propose the definition of Mittag-Leffler stability and introduce the fractional Lyapunov direct method. Then we provide the fractional comparison principle. Third, we extend the application of Riemann-Liouville fractional systems by using Caputo fractional systems. Finally, an illustrative example is provided as a proof of concept. keywords Fractional order dynamic system, Nona...

2008
Yuriy Povstenko

The time-fractional diffusion-wave equation is considered in a half-plane. The Caputo fractional derivative of the order 0 < α < 2 is used. Several examples of problems with Dirichlet and Neumann boundary conditions are solved using the Laplace integral transform with respect to time and the Fourier transforms with respect to spatial coordinates. The solution is written in terms of the Mittag-L...

2014
Luisa Beghin Claudio Macci Bashir Ahmad

and Applied Analysis 3 where the first term refers to the probability mass concentrated in the origin, δ y denotes the Dirac delta function, and fYβ denotes the density of the absolutely continuous component. The function gYβ given in 1.5 satisfies the following fractional master equation, that is, ∂ ∂tβ gYβ ( y, t ) −λgYβ ( y, t ) λ ∫ ∞ −∞ gYβ ( y − x, t ) fX x dx, 1.6 where ∂/∂t is the Caputo...

2016
Ahmad Fino Hassan Ibrahim Ahmad Z. FINO Hassan IBRAHIM

In this paper, we consider a nonhomogeneous space-time fractional telegraph equation defined in a bounded space domain, which is obtained from the standard telegraph equation by replacing the firstor second-order time derivative by the Caputo fractional derivative Dt , α > 0; and the Laplacian operator by the fractional Laplacian (−∆) , β ∈ (0, 2]. We discuss and derive the analytical solutions...

Journal: :J. London Math. Society 2016
Malcolm Brown Marco Marletta Freddy Symons

We prove a pair of uniqueness theorems for an inverse problem for an ordinary differential operator pencil of second order. The uniqueness is achieved from a discrete set of data, namely, the values at the points −n2 (n ∈ N) of (a physically appropriate generalization of) the Weyl– Titchmarsh m-function m(λ) for the problem. As a corollary, we establish a uniqueness result for a physically moti...

2008
Anne-Laure Basdevant Arvind Singh

We consider a one-dimensional transient cookie random walk. It is known from a previous paper [3] that a cookie random walk (Xn) has positive or zero speed according to some positive parameter α > 1 or ≤ 1. In this article, we give the exact rate of growth of (Xn) in the zero speed regime, namely: for 0 < α < 1, Xn/n α+1 2 converges in law to a Mittag-Leffler distribution whereas for α = 1, Xn(...

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