Results 71 to 80 of about 924,447 (216)

On the analyzing of bifurcation properties of the one‐dimensional Mackey–Glass model by using a generalized approach

Mathematical Methods in the Applied Sciences, EarlyView.
The goal of this work is to look at how a nonlinear model describes hematopoiesis and its complexities utilizing commonly used techniques with historical and material links. Based on time delay, the Mackey–Glass model is explored in two instances. To offer a range, the relevance of the parameter impacting stability (bifurcation) is recorded.
Shuai Zhang, Yaya Wang, Hongyin Geng, Wei Gao, Esin Ilhan, Haci Mehmet Baskonus   +5 more
wiley   +1 more source

A fractional equation with left-sided fractional Bessel derivatives of Gerasimov-Caputo type [PDF]

, 2019
In this article we propose and study a method to solve ordinary differential equations with left-sided fractional Bessel derivatives on semi-axes of Gerasimov-Caputo type.
Elina Shishkina, Shishkina, E., Sergey Sitnik, Sitnik, S.   +3 more
core   +1 more source

A highly accurate numerical method for solving boundary value problem of generalized Bagley‐Torvik equation

Mathematical Methods in the Applied Sciences, EarlyView.
A highly accurate numerical method is given for the solution of boundary value problem of generalized Bagley‐Torvik (BgT) equation with Caputo derivative of order 0<β<2$$ 0<\beta <2 $$ by using the collocation‐shooting method (C‐SM). The collocation solution is constructed in the space Sm+1(1)$$ {S}_{m+1}^{(1)} $$ as piecewise polynomials of degree at ...
Suzan Cival Buranay, Mtema James Chin, Nazim I. Mahmudov   +2 more
wiley   +1 more source

On Caputo modification of the Hadamard fractional derivatives [PDF]

Advances in Difference Equations, 2014
Abstract This paper is devoted to the study of Caputo modification of the Hadamard fractional derivatives. From here and after, by Caputo-Hadamard derivative, we refer to this modified fractional derivative (Jarad et al. in Adv. Differ. Equ. 2012:142, 2012, p.7). We present the generalization of the fundamental theorem of fractional calculus (
Yusuf Y. Gambo, Fahd Jarad, Dumitru Băleanu, Thabet Abdeljawad   +3 more
openaire   +1 more source

Exponential Stability of Higher Order Fractional Neutral Stochastic Differential Equation Via Integral Contractors

Mathematical Methods in the Applied Sciences, Volume 48, Issue 6, Page 6425-6446, April 2025.
ABSTRACT The well‐posedness results for mild solutions to the fractional neutral stochastic differential system with Rosenblatt process with Hurst index Ĥ∈12,1$$ \hat{H}\in \left(\frac{1}{2},1\right) $$ is discussed in this article. To demonstrate the results, the concept of bounded integral contractors is combined with the stochastic result and ...
Dimplekumar N. Chalishajar, Dhanalakshmi Kasinathan, Ramkumar Kasinathan, Ravikumar Kasinathan   +3 more
wiley   +1 more source

A new crossover dynamics mathematical model of monkeypox disease based on fractional differential equations and the Ψ-Caputo derivative: Numerical treatments

Alexandria Engineering Journal
A novel crossover model for monkeypox disease that incorporates Ψ-Caputo fractional derivatives is presented here, where we use a simple nonstandard kernel function Ψ(t).
N.H. Sweilam, S.M. Al-Mekhlafi, W.S. Abdel Kareem, G. Alqurishi   +3 more
doaj   +1 more source

Boundary Value Problem for Impulsive Delay Fractional Differential Equations with Several Generalized Proportional Caputo Fractional Derivatives

, 2023
A scalar nonlinear impulsive differential equation with a delay and generalized proportional Caputo fractional derivatives (IDGFDE) is investigated. The linear boundary value problem (BVP) for the given fractional differential equation is set up.
Ravi P. Agarwal, Snezhana Hristova
core   +1 more source

Equivalences of Nonlinear Higher Order Fractional Differential Equations With Integral Equations

Mathematical Methods in the Applied Sciences, Volume 48, Issue 6, Page 6930-6942, April 2025.
ABSTRACT Equivalences of initial value problems (IVPs) of both nonlinear higher order (Riemann–Liouville type) fractional differential equations (FDEs) and Caputo FDEs with the corresponding integral equations are studied in this paper. It is proved that the nonlinearities in the FDEs can be L1$$ {L}^1 $$‐Carathéodory with suitable conditions.
Kunquan Lan
wiley   +1 more source

Exact results for a fractional derivative of elementary functions

SciPost Physics, 2018
We present exact analytical results for the Caputo fractional derivative of a wide class of elementary functions, including trigonometric and inverse trigonometric, hyperbolic and inverse hyperbolic, Gaussian, quartic Gaussian, and Lorentzian ...
Gavriil Shchedrin, Nathanael C. Smith, Anastasia Gladkina, Lincoln D. Carr
doaj   +1 more source

Existence and Stability Analysis of Classical and Fractional‐Order Generalized Brusselator Reaction‐Diffusion System

Mathematical Methods in the Applied Sciences, EarlyView.
ABSTRACT The present work is devoted to establishing existence results and examining the stability properties of solutions associated with a generalized Brusselator reaction–diffusion system in both the classical and fractional‐order settings. The corresponding ODE and PDE formulations are considered to establish the global existence of solutions in ...
Fadia Haouam, Lamia Djebara, Salem Abdelmalek, Mokhtar Kirane   +3 more
wiley   +1 more source