Results 111 to 120 of about 372,508 (154)

A normalized Caputo–Fabrizio fractional diffusion equation

AIMS Mathematics
We propose a normalized Caputo–Fabrizio (CF) fractional diffusion equation. The CF fractional derivative replaces the power-law kernel in the Caputo derivative with an exponential kernel, which avoids singularities. Compared to the Caputo derivative, the
Junseok Kim
doaj   +1 more source

Consensus of Multiagent Systems Described by Various Noninteger Derivatives

Complexity, 2019
In this paper, we unify and extend recent developments in Lyapunov stability theory to present techniques to determine the asymptotic stability of six types of fractional dynamical systems.
G. Nava-Antonio, G. Fernández-Anaya, E. G. Hernández-Martínez, J. J. Flores-Godoy, E. D. Ferreira-Vázquez   +4 more
doaj   +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 generalized Hilfer-type fractional derivative with applications to space-time diffusion equation

Results in Physics, 2021
This paper is concerned to present and apply a new generalized fractional derivative, that is the Generalized Hilfer-type (GH) fractional derivative.
Tahir Ullah Khan, Muhammad Adil Khan, Yu-Ming Chu   +2 more
doaj  

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

The general Caputo–Katugampola fractional derivative and numerical approach for solving the fractional differential equations

Alexandria Engineering Journal
In this manuscript, we present the general fractional derivative (FD) along with its fractional integral (FI), specifically the ψ-Caputo–Katugampola fractional derivative (ψ-CKFD).
Lakhlifa Sadek, Sahar Ahmed ldris, Fahd Jarad   +2 more
doaj  

Survey and new results on boundary-value problems of singular fractional differential equations with impulse effects

Electronic Journal of Differential Equations, 2016
Firstly we prove existence and uniqueness of solutions of Cauchy problems of linear fractional differential equations (LFDEs) with two variable coefficients involving Caputo fractional derivative, Riemann-Liouville derivative, Caputo type Hadamard ...
Yuji Liu
doaj  

Homotopy Perturbation ρ-Laplace Transform Method and Its Application to the Fractional Diffusion Equation and the Fractional Diffusion-Reaction Equation

Fractal and Fractional, 2019
In this paper, the approximate solutions of the fractional diffusion equations described by the fractional derivative operator were investigated. The homotopy perturbation Laplace transform method of getting the approximate solution was proposed.
Ndolane Sene, Aliou Niang Fall
doaj   +1 more source

Quasi‐Diffusion Imaging: Application to Ultra‐High b‐Value and Time‐Dependent Diffusion Images of Brain Tissue

NMR in Biomedicine, Volume 38, Issue 4, April 2025.
Quasi‐Diffusion Imaging (QDI) signal transitions from stretched exponential to negative power law behaviour at ultra‐high b‐values via an inflection point (data and fits shown for representative (a) grey and (b) white matter voxels). QDI is parameterised by the (c) diffusion coefficient, D1,2 (in mm2s−1) and (d) apparent exponent, α, allowing ...
Thomas R. Barrick, Carson Ingo, Matt G. Hall, Franklyn A. Howe   +3 more
wiley   +1 more source

On proportional hybrid operators in the discrete setting

Mathematical Methods in the Applied Sciences, Volume 48, Issue 4, Page 4344-4364, 15 March 2025.
In this article, we introduce a new nonlocal operator Hα$$ {H}^{\alpha } $$ defined as a linear combination of the discrete fractional Caputo operator and the fractional sum operator. A new dual operator Rα$$ {R}^{\alpha } $$ is also introduced by replacing the discrete fractional Caputo operator with the discrete fractional Riemann ...
Carlos Lizama, Marina Murillo‐Arcila
wiley   +1 more source