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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, 2005The 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 +2 more
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Heisenberg’s uncertainty principle associated with the Caputo fractional derivative
Journal of Mathematical Physics, 2021In 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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Remarks on the initialization of Caputo derivative
Proceedings of 2012 IEEE/ASME 8th IEEE/ASME International Conference on Mechatronic and Embedded Systems and Applications, 2012In this paper, we have further discussed the initialization issue of Caputo derivative. Specially, based on an initialization theory established by Lorenzo and Hartley, we give a new result about the initialization function of Caputo derivative under the assumption of terminal initialization.
Fengrong Zhang, Changpin Li
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Communications in nonlinear science & numerical simulation, 2020
While for the integer-order derivatives, the commutative and semigroup (or associative) properties hold, the same is not true, in general, for the fractional derivatives. We show that, when the function is analytic, the Caputo derivative enjoys the above
L. Beghin, M. Caputo
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While for the integer-order derivatives, the commutative and semigroup (or associative) properties hold, the same is not true, in general, for the fractional derivatives. We show that, when the function is analytic, the Caputo derivative enjoys the above
L. Beghin, M. Caputo
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Complete infinitesimal prolongation of the Riemann–Liouville and Caputo derivatives
Reviews in Mathematical Physics, 2023This paper presents the infinitesimal prolongation to Riemann–Liouville and Caputo fractional derivatives without the restrictive lower limit fixed in the integrals, when applicated to the transformation group. The properties are presented, and the examples are illustrated along with the symmetry to fractional derivative criteria.
Felix S. Costa +4 more
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Automatic initialization of the Caputo fractional derivative
IEEE Conference on Decision and Control and European Control Conference, 2011Initialization 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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Three Kinds of Discrete Formulae for the Caputo Fractional Derivative
Communications on Applied Mathematics and Computation, 2022zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Zhengnan Dong +3 more
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The Caputo Derivative And The Infinite State Approach
IFAC Proceedings Volumes, 2013Abstract This paper presents the interpretation of the Caputo derivative with the help of the infinite state approach, also known as the fractional integrator approach. After presentation of the modified Laplace transform equations, definition of state variables is discussed, as well as its application to the characterization of fractional system ...
Trigeassou Jean-Claude +2 more
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Modeling the dynamics of hepatitis E via the Caputo–Fabrizio derivative
Mathematical Modelling of Natural Phenomena, 2019A virus that causes hepatitis E is known as (HEV) and regarded on of the reason for lever inflammation. In mathematical aspects a very low attention has been paid to HEV dynamics.
M. Khan, Z. Hammouch, D. Baleanu
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IEEE Transactions on Circuits and Systems I: Regular Papers, 2021
This study employs the Caputo-Fabrizio fractional derivative to determine the model of fractional-order RC circuits with arbitrary voltage input which can be widely used in a variety of electrical systems. Analog circuit implementation of fractional-order RC circuits defined by Caputo-Fabrizio fractional derivative is presented and verified by ...
Da Lin +7 more
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This study employs the Caputo-Fabrizio fractional derivative to determine the model of fractional-order RC circuits with arbitrary voltage input which can be widely used in a variety of electrical systems. Analog circuit implementation of fractional-order RC circuits defined by Caputo-Fabrizio fractional derivative is presented and verified by ...
Da Lin +7 more
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