Results 71 to 80 of about 10,260 (153)

Heterogeneous Media Heat Transfer Simulations Based on 3D‐Fractional Parametric Laplace Kernel

International Journal of Differential Equations, Volume 2026, Issue 1, 2026.
This paper introduces a new Mittag–Leffler–Laplace memory kernel defined by Φ˜μ,ν,κα,ρs=∫0∞Eρ−μξκ/κξνα−1e−sξdξ, s>0, and develops a unified framework for modeling heat transfer in heterogeneous media with nonlocal temporal memory. The proposed kernel combines algebraic singularity, stretched attenuation, and fractional relaxation through independent ...
Rabha W. Ibrahim, Ali A. Jizany, Hasan Kahtan, Elena Kaikina   +3 more
wiley   +1 more source

Models based on Mittag-Leffler functions for anomalous relaxation in dielectrics

, 2011
We revisit the Mittag-Leffler functions of a real variable $t$, with one, two and three order-parameters $\{\alpha, \beta, \gamma\}$, as far as their Laplace transform pairs and complete monotonicty properties are concerned. These functions, subjected to
de Oliveira, Edmundo Capelas, Mainardi, Francesco, Vaz Jr, Jayme   +2 more
core   +1 more source

A Morgan‐Voyce Polynomial Framework for Solving Variable‐Order Atangana–Baleanu Fractional Differential Equations

International Journal of Differential Equations, Volume 2026, Issue 1, 2026.
This paper presents a novel and efficient spectral collocation framework for solving nonlinear variable‐order fractional differential equations (VO‐FDEs) involving the Atangana–Baleanu–Caputo (ABC) operator. Shifted Morgan‐Voyce polynomials (SMVPs) are employed as basic functions to construct a new operational matrix specifically adapted to the ...
Ghadah S. E. Noman, D. D. Pawar, Sining Zheng   +2 more
wiley   +1 more source

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

Lyapunov Stability and Optimization of a Fractional‐Order HIV/AIDS Model Coupling Vertical Transmission With Saturated Treatment

International Journal of Mathematics and Mathematical Sciences, Volume 2026, Issue 1, 2026.
This research introduces a fractional‐order nonlinear model for the dynamics of human immunodeficiency virus (HIV) and acquired immune deficiency syndrome (AIDS) using Caputo‐type derivatives of noninteger order. Solution properties of the model are investigated by analyzing positivity and boundedness characteristics via the generalized mean value ...
Sulaimon F. Abimbade, Furaha M. Chuma, Samson Olaniyi, Adekunle O. Sangotola, Gideon K. Gogovi, Shikha Binwal   +5 more
wiley   +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

Certain unified integral formulas involving five-parameter Mittag-Leffler function

International Journal of Mathematics for Industry
In this work, we propose some unified integral representations for the five-parameter Mittag-Leffler function, and our findings are evaluated in terms of various generalized special functions.
Ankit Pal, Vinod Kumar Jatav, Udai Kumar
doaj   +1 more source

Composition Formula for Saigo Fractional Calculus Operator on  p R q  Function

International Journal of Mathematics and Mathematical Sciences, Volume 2026, Issue 1, 2026.
In this paper, we use the Saigo operators to create fractional integral and derivative formulations involving the generalized p R q function. The resulting expressions are represented using generalized Wright hypergeometric functions. We develop various results for fractional integrals and derivatives of the Weyl, Erdélyi–Kober, Saigo, and Riemann ...
Belete Debalkie, D. L. Suthar, Rodica D. Costin   +2 more
wiley   +1 more source

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

A Generalized q-Mittag-Leffler Function by q-Captuo Fractional Linear Equations

Abstract and Applied Analysis, 2012
Some Caputo q-fractional difference equations are solved. The solutions are expressed by means of a new introduced generalized type of q-Mittag-Leffler functions. The method of successive approximation is used to obtain the solutions.
Thabet Abdeljawad, Betül Benli, Dumitru Baleanu   +2 more
doaj   +1 more source