Results 251 to 260 of about 58,917 (294)

Fractional viscoelastic models with Caputo generalized fractional derivative

Mathematical Methods in the Applied Sciences, 2021
This article focuses on fractional Maxwell model of viscoelastic materials, which are a generalization of classic Maxwell model to noninteger order derivatives. We present and discuss formulations of the fractional order viscoelastic model and give physical interpretations of the model by using viscoelastic functions.
Nikita Bhangale, Krunal B. Kachhia, J. F. Gómez‐Aguilar   +2 more
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Fractional conformable derivatives of Liouville–Caputo type with low-fractionality

Physica A: Statistical Mechanics and its Applications, 2018
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Morales-Delgado, V. F., Gómez-Aguilar, J. F., Escobar-Jiménez, R. F., Taneco-Hernández, M. A.   +3 more
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To the Theory of Differential Inclusions with Caputo Fractional Derivatives

Differential Equations, 2020
The paper studies a Cauchy problem associated to fractional differential inclusions of the form \[ ^CD^{\alpha }x(t)\in F(t,x(t)),\quad a.e.\; t\in [t_0,T], \] \[ x(t)=w_0(t),\quad t\in [0,t_0], \] where \(\alpha \in (0,1)\), \(^CD^{\alpha }\) denotes Caputo's fractional derivative, \(F:[0,T]\times {\mathbb{R}}^n\to \mathcal{P}({\mathbb{R}}^n)\) is a ...
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Approximations of fractional integrals and Caputo fractional derivatives

Applied Mathematics and Computation, 2006
In a series of recent papers [see \textit{K. Diethelm, A. D. Freed} and \textit{N. J. Ford}, Numer. Algorithms 36, No. 1, 31--52 (2004; Zbl 1055.65098)], and the references cited therein], the reviewer and his collaborators have proposed and analysed a numerical scheme for the approximation of \(J^\alpha\), the Riemann-Liouville fractional integral of ...
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Three Kinds of Discrete Formulae for the Caputo Fractional Derivative

Communications on Applied Mathematics and Computation, 2022
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Zhengnan Dong, Enyu Fan, Ao Shen, Yuhao Su   +3 more
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Initialization Issues of the Caputo Fractional Derivative

Volume 6: 5th International Conference on Multibody Systems, Nonlinear Dynamics, and Control, Parts A, B, and C, 2005
The importance of proper initialization in taking into account the history of a system whose time evolution is governed by a differential equation of fractional order, has been established by Lorenzo and Hartley, who also gave the method of properly incorporating the effect of the past (history) by means of an initialization function for the Riemann ...
B. N. Narahari Achar, Carl F. Lorenzo, Tom T. Hartley   +2 more
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Caputo fractional derivative of $$\alpha $$-fractal spline

Numerical Algorithms
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Priyanka, T. M. C., Gowrisankar, A., Prasad, M. Guru Prem, Liang, Yongshun, Cao, Jinde   +4 more
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Automatic initialization of the Caputo fractional derivative

IEEE Conference on Decision and Control and European Control Conference, 2011
Initialization of Riemann-Liouville and Caputo fractional derivatives remains an open research topic. These fractional derivatives are fundamentally related to fractional integration operators, so their initial conditions are the initial state vector of the associated fractional integrators.
J-C. Trigeassou, N. Maamri, A. Oustaloup
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Heisenberg’s uncertainty principle associated with the Caputo fractional derivative

Journal of Mathematical Physics, 2021
In this paper, we establish the Heisenberg’s uncertainty inequality associated with the Caputo derivative of order q ∈ (1, ∞) in the generalized Bargmann–Fock space. We also determine exactly when the equality occurs in the uncertainty inequality. It is done by estimating the growth of the eigenvalues of the commutator [Dq,zq].
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Fractional Constrained Systems and Caputo Derivatives

Journal of Computational and Nonlinear Dynamics, 2008
During the last few years, remarkable developments have been made in the theory of the fractional variational principles and their applications to control problems and fractional quantization issue. The variational principles have been used in physics to construct the phase space of a fractional dynamical system.
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