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Fractional calculus and generalized Mittag-Leffler type functions

, 2017
version 2 (mise à jour)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 ...
Lavault, Christian
core   +1 more source

Generalized Mittag-Leffler Input Stability of the Fractional Differential Equations

, 2019
The behavior of the analytical solutions of the fractional differential equation described by the fractional order derivative operators is the main subject in many stability problems.
Ndolane Sene, Gautam Srivastava
core   +1 more source

Anomalous diffusion of fractional harmonic oscillator driven by additive impulsive noise

四川大学学报. 自然科学版, 2017
Anomalous diffusion of a fractional harmonic oscillator driven by both thermal noise and additive impulsive noise is investigated. By using the Laplace and double Laplace transform techniques, the mean, variance, correlation function and mean square ...
ZHOU Xing-Wang, ZHONG Ji-Yu
doaj  

On a recurrence relation of generalized Mittag-Leffler function

Surveys in Mathematics and its Applications, 2009
Summary: The principal aim of this paper is to investigate a recurrence relation and an integral representation of generalized Mittag-Leffler function \(E_{\alpha ,\beta }^{\gamma ,q}(z)\). At the end several special cases are also discussed.
Ajay K. Shukla, Jyotindra C. Prajapati
openaire   +2 more sources

A General Class of Multivariable Mittag–Leffler Function and Its Associated Applications

Abstract and Applied Analysis
In this paper, a new class of multivariable special functions and their generalizations is introduced and used to solve generalized fractional differential and kinetic equations.
B. B. Jaimini, null Meenu, Suman Sharma, S. D. Purohit, D. L. Suthar   +4 more
doaj   +1 more source

LAPLACE TRANSFORMATION AND MITTAG-LEFFLER FUNCTION FOR THE SOLUTION OF DAMPED OSCILLATOR EQUATION WITH FRACTIONAL ORDER

Barekeng
Fractional calculus has emerged as an active area of research due to its ability to model complex dynamical systems with memory effects and anomalous diffusion.
Gusrian Putra, Meysi Supmawati, Lutfi Mardianto   +2 more
doaj   +1 more source

Some Remarks on Estimate of Mittag-Leffler Function

, 2019
The estimate of Mittag-Leffler function has been widely applied in the dynamic analysis of fractional-order systems in some recently published papers. In this paper, we show that the estimate for Mittag-Leffler function is not correct.
Zhen Wang, Jia Jia, Xia Huang, Yunliang Wei   +3 more
core   +1 more source

SOME REMARKS ON GENERALIZED MITTAG-LEFFLER FUNCTION

, 2009
The principal aim of the paper is to establish the function and its properties by using Fractional Calculus. We also obtained some integral representations of the function which is recently introduced by Shukla and Prajapati[6].
SHUKLA, AJAY K, PRAJAPATI, JYOTINDRA C
openaire   +1 more source

Generalized Mittag-Leffler Function: Properties in Fractional Calculus and Integral Transforms [PDF]

In this work, we introduce a new generalized Mittag-Leffler function defined via the extended Beta function and establish its integral and differential representations.
Z. Bin-Alhag, Ali, Bin-Saad, Maged G.
core   +1 more source

Geometric Structures and Inclusion Properties of Multivalent Mittag-Leffler-Type Poisson Subfamilies

Mathematics
The interplay between special functions and geometric function theory continues to inspire significant advances in the study of analytic and multivalent functions.
Feras Yousef, Tariq Al-Hawary, Ibtisam Aldawish   +2 more
doaj   +1 more source