نتایج جستجو برای: leffler

تعداد نتایج: 1008  

Journal: :Miskolc Mathematical Notes 2017

Journal: :Journal of Inequalities and Applications 2023

Abstract In this paper, we propose a generalized Gronwall inequality in the context of ψ -Hilfer proportional fractional derivative. Using Picard’s successive approximation and definition Mittag–Leffler functions, construct representation formula solution for differential equation with constant coefficient form kernel. The uniqueness result is proved by using Banach’s fixed-point theorem some p...

The study of the stability of differential equations without its explicit solution is of particular importance. There are different definitions concerning the stability of the differential equations system, here we will use the definition of the concept of Lyapunov. In this paper, first we investigate stability analysis of distributed order fractional differential equations by using the asympto...

2016
Corina Constantinescu Gennady Samorodnitsky Wei Zhu

In this paper we provide three equivalent expressions for ruin probabilities in a Cramér-Lundberg model with gamma distributed claims. The results are solutions of integro-differential equations, derived by means of (inverse) Laplace transforms. All the three formulas have infinite series forms, two involving Mittag-Leffler functions and the third one involving moments of the claims distributio...

2014
Dinesh Kumar Sunil Kumar

We introduce and study a new function called R-function, which is an extension of the generalized Mittag-Leffler function. We derive the relations that exist between the R-function and Saigo fractional calculus operators. Some results derived by Samko et al. (1993), Kilbas (2005), Kilbas and Saigo (1995), and Sharma and Jain (2009) are special cases of the main results derived in this paper.

2015
Daniel A. Leffler Anna Sapone Rupa Mukherjee

Anna Sapone MD PhD, Celiac Center, Division of Gastroenterology Daniel A. Leffler MD, MS, Director of Clinical Research, Celiac Center, Director of Quality Improvement, Associate Professor of Medicine at Harvard Medical School, Division of Gastroenterology Rupa Mukherjee MD, Celiac Center, Division of Gastroenterology, Department of Medicine, Instructor in Medicine at Harvard Medical School, Be...

2012
Seetha Lekshmi Catherine Thomas

In this paper we make an attempt to review count data models developed so far as generalizations of Poisson process. We consider Winkleman’s gamma count model and the Weibull count model of Mc Shane et al. The fractional generalization of Poisson process by Mainardi et al. is also considered. A Mittag-Leffler count model is developed and studied in detail. Simulation studies are also conducted.

2007
Rudolf GORENFLO Francesco MAINARDI

To offer a view into the rapidly developing theory of fractional diffusion processes we describe in some detail three topics of present interest: (i) the well-scaled passage to the limit from continuous time random walk under power law assumptions to space-time fractional diffusion, (ii) the asymptotic universality of the Mittag-Leffler waiting time law in time-fractional processes, (iii) our m...

Journal: :Physical review. E, Statistical, nonlinear, and soft matter physics 2002
Mark M Meerschaert David A Benson Hans-Peter Scheffler Boris Baeumer

Classical and anomalous diffusion equations employ integer derivatives, fractional derivatives, and other pseudodifferential operators in space. In this paper we show that replacing the integer time derivative by a fractional derivative subordinates the original stochastic solution to an inverse stable subordinator process whose probability distributions are Mittag-Leffler type. This leads to e...

Journal: :Physical review. E, Statistical, nonlinear, and soft matter physics 2006
A D Viñales M A Despósito

We study the effect of a disordered or fractal environment in the irreversible dynamics of a harmonic oscillator. Starting from a generalized Langevin equation and using Laplace analysis, we derive exact expressions for the mean values, variances, and velocity autocorrelation function of the particle in terms of generalized Mittag-Leffler functions. The long-time behaviors of these quantities a...

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