Results 61 to 70 of about 10,320 (199)

Extension of Mittag-Leffler function

, 2017
In this paper, we present an extension of Mittag-Leffler function by using the extension of beta functions ( zergin et al. in J. Comput. Appl. Math. 235 (2011), 4601-4610) and obtain some integral representation of this newly defined function.
Rahman, G., Nisar, K. S., Mubeen, S., Arshad, M.   +3 more
openaire   +2 more sources

Neuronal Dynamics of an Intrinsically Bursting Neuron Through the Caputo–Fabrizio Fractal–Fractional Hodgkin–Huxley Model

International Journal of Differential Equations, Volume 2026, Issue 1, 2026.
This study introduces a novel fractal–fractional extension of the Hodgkin–Huxley model to capture complex neuronal dynamics, with particular focus on intrinsically bursting patterns. The key innovation lies in the simultaneous incorporation of Caputo–Fabrizio operators with fractional order α for memory effects and fractal dimension τ for temporal ...
M. J. Islam, M. J. Abedin, A. Hoque, M. G. Hafez, Jaume Giné   +4 more
wiley   +1 more source

Solutions of the Fractional Reaction Equation and the Fractional Diffusion Equation

, 2009
In view of the role of reaction equations in physical problems, the authors derive the explicit solution of a fractional reaction equation of general character, that unifies and extends earlier results.
Haubold, H. J., Mathai, A. M., Saxena, R. K.   +2 more
core   +1 more source

Comparison of Integer‐, Constant‐, and Variable‐Order Fractional Models of Competition for Student Population Using Caputo–Fabrizio Fractional Derivative With Policy Interventions

International Journal of Mathematics and Mathematical Sciences, Volume 2026, Issue 1, 2026.
This study develops constant‐order (CO) and variable‐order (VO) Caputo–Fabrizio (CF) fractional derivative (CFFD) models to extend the classical integer‐order framework for analyzing competition among public, private, and nonenrolled student populations under varying policy intervention intensities.
Kiprotich Ezra Bett, Cyrus Gitonga Ngari, Grace Gakii Muthuri, Kareem Elgindy   +3 more
wiley   +1 more source

Fractional operators with generalized Mittag-Leffler k-function

Advances in Difference Equations, 2019
In this paper, our main aim is to deal with two integral transforms involving the Gauss hypergeometric functions as their kernels. We prove some composition formulas for such generalized fractional integrals with Mittag-Leffler k-function.
Shahid Mubeen, Rana Safdar Ali
doaj   +1 more source

Integral representations of Mittag-Leffler function on the positive real axis

Trends in Computational and Applied Mathematics, 2019
The Mittag-Leffler functions appear in many problems associated with fractional calculus. In this paper, we use the methodology for evaluation of the inverse Laplace transform, proposed by M. N.
Eliana Contharteze Grigoletto, Edmundo Capelas Oliveira, Rubens Figueiredo Camargo   +2 more
doaj   +1 more source

Fractional Stokes-Boussinesq-Langevin equationand Mittag-Leffler correlation decay [PDF]

, 2017
his paper presents some stationary processes which are solutions of the fractional Stokes-Boussinesq-Langevin equation. These processes have reflection positivity and their correlation functions, which may exhibit the Alder-Wainwright effect or long ...
Anh, V. V., Leonenko, Nikolai N.
core  

Continuous time random walk, Mittag-Leffler waiting time and fractional diffusion: mathematical aspects

, 2007
We show the asymptotic long-time equivalence of a generic power law waiting time distribution to the Mittag-Leffler waiting time distribution, characteristic for a time fractional CTRW.
Gorenflo, Rudolf, Mainardi, Francesco
core   +3 more sources

Solution of Caputo Generalized Bagley–Torvik Equation Using the Tarig Transform

Journal of Applied Mathematics, Volume 2026, Issue 1, 2026.
A fractional‐order differential equation called the Bagley–Torvik equation describes the behavior of viscoelastic damping. We employed the newly defined Tarig transform in this study to find the analytic solution to the Caputo generalized Bagley–Torvik equation.
Lata Chanchlani, Manisha, D. L. Suthar, S. D. Purohit, Ahmed Saoudi   +4 more
wiley   +1 more source

Certain Properties Associated with Generalized $M$-Series using Hadamard Product [PDF]

Sahand Communications in Mathematical Analysis
The generalized $M$-series is a hybrid function of generalized Mittag-Leffler function and generalized hypergeometric function.  The principal aim of this paper is to investigate certain properties resembling those of the Mittag-Leffler and ...
Dheerandra Sachan, Dinesh Kumar, Kottakkaran Nisar   +2 more
doaj   +1 more source