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Unexpected behavior of Caputo fractional derivative [PDF]
Computational and Applied Mathematics, 2016 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Robinson Tavoni +1 more
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A new fractional integral associated with the Caputo–Fabrizio fractional derivative
Rendiconti del Circolo Matematico di Palermo Series 2, 2020zbMATH Open Web Interface contents unavailable due to conflicting licenses.
M. Moumen Bekkouche +3 more
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Variational Problems Involving a Caputo-Type Fractional Derivative [PDF]
Journal of Optimization Theory and Applications, 2016 The aim of this paper is to study certain problems of calculus of variations, that are dependent upon a Lagrange function on a Caputo-type fractional derivative. This type of fractional operator is a generalization of the Caputo and the Caputo--Hadamard fractional derivatives, that are dependent on a real parameter ro.
Ricardo Almeida
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Caputo fractional derivative of $$\alpha $$-fractal spline
Numerical AlgorithmszbMATH Open Web Interface contents unavailable due to conflicting licenses.
T. M. C. Priyanka +4 more
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Fractional conformable derivatives of Liouville–Caputo type with low-fractionality
Physica A: Statistical Mechanics and its Applications, 2018zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Morales-Delgado, V. F. +3 more
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To the Theory of Differential Inclusions with Caputo Fractional Derivatives
Differential Equations, 2020The 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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Caputo-Based Fractional Derivative in Fractional Fourier Transform Domain
IEEE Journal on Emerging and Selected Topics in Circuits and Systems, 2013This paper proposes a novel closed-form analytical expression of the fractional derivative of a signal in the Fourier transform (FT) and the fractional Fourier transform (FrFT) domain by utilizing the fundamental principles of the fractional order calculus.
Kulbir Singh +2 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, 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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The Peano–Sard theorem for Caputo fractional derivatives and applications
Journal of Computational and Applied MathematicszbMATH Open Web Interface contents unavailable due to conflicting licenses.
Arran Fernandez, Suzan Cival Buranay
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Fractional Constrained Systems and Caputo Derivatives
Journal of Computational and Nonlinear Dynamics, 2008During 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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