Results 51 to 60 of about 2,052,042 (321)

Coupled systems of fractional equations related to sound propagation: analysis and discussion [PDF]

, 2012
In this note we analyse the propagation of a small density perturbation in a one-dimensional compressible fluid by means of fractional calculus modelling, replacing thus the ordinary time derivative with the Caputo fractional derivative in the ...
Diethelm K., Federico Polito, Fellah Z. E. A., Haubold H. J., Kilbas A. A., Podlubny I., Roberto Garra   +6 more
core   +1 more source

Analysis of Cauchy Problems and Diffusion Equations Associated with the Hilfer–Prabhakar Fractional Derivative via Kharrat–Toma Transform

Fractal and Fractional, 2023
In this paper, the Kharrat–Toma transforms of the Prabhakar integral, a Hilfer–Prabhakar (HP) fractional derivative, and the regularized version of the HP fractional derivative are derived.
Ved Prakash Dubey, Jagdev Singh, Sarvesh Dubey, Devendra Kumar   +3 more
doaj   +1 more source

A mathematical model for COVID-19 transmission by using the Caputo fractional derivative

Chaos, Solitons & Fractals, 2020
Highlights • COVID-19 is transmitted from asymptomatic individuals to susceptible individuals.• COVID-19 is transmitted from symptomatic individuals to susceptible individuals.• Since R0=1.6 is greater than 1, the COVID-19 will spread exponentially.• If ...
N. Tuan, H. Mohammadi, S. Rezapour
semanticscholar   +1 more source

Comparative study of integer-order and fractional-order artificial neural networks: Application for mathematical function generation

e-Prime: Advances in Electrical Engineering, Electronics and Energy
This paper investigates the impact of fractional derivatives on the activation functions of an artificial neural network (ANN). Based on the results and analysis, a three-layer backpropagation neural network model with fractional and integer derivatives ...
Manisha Premkumar Joshi, Savita Bhosale, Vishwesh A. Vyawahare   +2 more
doaj   +1 more source

Numerical simulation of variable-order fractal-fractional delay differential equations with nonsingular derivative

Engineering Science and Technology, an International Journal, 2023
This work develops a new Legendre delay operational matrix based on Legendre polynomial features that are integrated with regard to the Legendre fractional derivative operational matrix in order to solve the issues.
Mays Basim, Ali Ahmadian, Norazak Senu, Zarina Bibi Ibrahim   +3 more
doaj   +1 more source

An analytical solution for the Caputo type generalized fractional evolution equation

Alexandria Engineering Journal, 2022
The Caputo type generalized fractional evolution equation is studied in this paper. Since the Caputo type generalized fractional derivative is well-known for being the generalization of Caputo fractional derivatives, this article’s studies contribute to ...
Wannika Sawangtong, Panumart Sawangtong
doaj   +1 more source

A new Riemann–Liouville type fractional derivative operator and its application in generating functions

Advances in Difference Equations, 2018
Here, the concept of a new and interesting Riemann–Liouville type fractional derivative operator is exploited. Treatment of a fractional derivative operator has been made associated with the extended Appell hypergeometric functions of two variables and ...
M. Shadab, M. Faisal Khan, J. Luis Lopez-Bonilla   +2 more
doaj   +1 more source

Continuous grey model with conformable fractional derivative [PDF]

Chaos, Solitons & Fractals, 2020
Fractional-order grey models have received more attention owing to superiority to integer-order ones in terms of the prediction performance. In this paper, to further improve the performance of grey-based model, a new method based on conformable ...
Wanli Xie, Caixia Liu, Wen-ze Wu, Weidong Li, Chong Liu   +4 more
semanticscholar   +1 more source

Fractional Cauchy problems on bounded domains: survey of recent results

, 2010
In a fractional Cauchy problem, the usual first order time derivative is replaced by a fractional derivative. This problem was first considered by \citet{nigmatullin}, and \citet{zaslavsky} in $\mathbb R^d$ for modeling some physical phenomena.
A Einstein, AN Kochubei, AN Kochubei, AN Kochubei, AN Kochubei, B Baeumer, G Zaslavsky, Gilbarg D, Trudinger NS (2001) Elliptic partial differential equations of second order. Reprint of the, HL Royden, I Podlubny, J Bertoin, K Miller, KI Sato, M Caputo, M Naber, MM Meerschaert, MM Meerschaert, MM Meerschaert, MM Meerschaert, MM Meerschaert, MM Meerschaert, OP Agrawal, R Gorenflo, R Gorenflo, R Metzler, RF Bass, RR Nigmatullin, S Samko, W Arendt, WR Schneider   +29 more
core   +1 more source

FRACTIONAL CENTRAL DIFFERENCES AND DERIVATIVES [PDF]

IFAC Proceedings Volumes, 2006
Fractional central differences and derivatives are studied in this article. These are generalisations to real orders of the ordinary positive (even and odd) integer order differences and derivatives, and also coincide with the well known Riesz potentials.
openaire   +2 more sources