Results 31 to 40 of about 563,717 (299)

Fractional Order Barbalat’s Lemma and its Applications in the Stability of Fractional Order Nonlinear Systems

Mathematical Modelling and Analysis, 2017
This paper investigates fractional order Barbalat’s lemma and its applications for the stability of fractional order nonlinear systems with Caputo fractional derivative at first.
Fei Wang, Yongqing Yang
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An Extension of the Picard Theorem to Fractional Differential Equations with a Caputo-Fabrizio Derivative

Journal of Function Spaces, 2021
In this paper, we consider fractional differential equations with the new fractional derivative involving a nonsingular kernel, namely, the Caputo-Fabrizio fractional derivative.
H. R. Marasi, A. Soltani Joujehi, H. Aydi   +2 more
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On the Fractional Derivative of Dirac Delta Function and Its Application

Advances in Mathematical Physics, 2020
The Dirac delta function and its integer-order derivative are widely used to solve integer-order differential/integral equation and integer-order system in related fields. On the other hand, the fractional-order system gets more and more attention.
Zaiyong Feng, Linghua Ye, Yi Zhang
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Spectral approximations to the fractional integral and derivative [PDF]

, 2012
In this paper, the spectral approximations are used to compute the fractional integral and the Caputo derivative. The effective recursive formulae based on the Legendre, Chebyshev and Jacobi polynomials are developed to approximate the fractional ...
Li, Changpin, Liu, Fawang, Fanhai Zeng, Changpin Li, Zeng, Fanhai, Fawang Liu   +5 more
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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

Simulation of fractionally damped mechanical systems by means of a Newmark-diffusive scheme [PDF]

, 2010
A Newmark-diffusive scheme is presented for the time-domain solution of dynamic systems containing fractional derivatives. This scheme combines a classical Newmark time-integration method used to solve second-order mechanical systems (obtained for ...
Matignon, Denis, Deü, J.-F., Deü, Jean-Francois, Matignon, D.   +3 more
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Heat conduction with fractional Cattaneo–Christov upper-convective derivative flux model [PDF]

, 2016
Fractional order derivatives are global operators for which the time fractional order derivative possesses memory character while the space ones reflects non-local behavior.
Liu, Fawang, Zheng, Liancun, Zhang, Xinxin, Liu, Lin   +3 more
core   +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
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Orthonormal piecewise Vieta-Lucas functions for the numerical solution of the one- and two-dimensional piecewise fractional Galilei invariant advection-diffusion equations

Journal of Advanced Research, 2023
Introduction: Recently, a new family of fractional derivatives called the piecewise fractional derivatives has been introduced, arguing that for some problems, each of the classical fractional derivatives may not be able to provide an accurate statement ...
Mohammad Hossein Heydari, Mohsen Razzaghi, Dumitru Baleanu   +2 more
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Fractal Derivatives, Fractional Derivatives and q-Deformed Calculus

Entropy, 2023
This work presents an analysis of fractional derivatives and fractal derivatives, discussing their differences and similarities. The fractal derivative is closely connected to Haussdorff’s concepts of fractional dimension geometry.
Airton Deppman, Eugenio Megías, Roman Pasechnik   +2 more
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