Results 11 to 20 of about 383,064 (247)
Local density of Caputo-stationary functions in the space of smooth functions [PDF]
ESAIM: COCV, 2017, 2016 We consider the Caputo fractional derivative and say that a function is Caputo-stationary if its Caputo derivative is zero. We then prove that any $C^k\big([0,1]\big)$ function can be approximated in $[0,1]$ by a a function that is Caputo-stationary in $[
Bucur, Claudia
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Exact results for a fractional derivative of elementary functions [PDF]
SciPost Physics, 2018 We present exact analytical results for the Caputo fractional derivative of a wide class of elementary functions, including trigonometric and inverse trigonometric, hyperbolic and inverse hyperbolic, Gaussian, quartic Gaussian, and Lorentzian ...
Gavriil Shchedrin, Nathanael C. Smith, Anastasia Gladkina, Lincoln D. Carr
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Fractional Differential Equations With Dependence on the Caputo–Katugampola Derivative [PDF]
Journal of Computational and Nonlinear Dynamics, 2016 In this paper, we present a new type of fractional operator, the Caputo–Katugampola derivative. The Caputo and the Caputo–Hadamard fractional derivatives are special cases of this new operator. An existence and uniqueness theorem for a fractional Cauchy-type problem, with dependence on the Caputo–Katugampola derivative, is proved.
Almeida, R. +2 more
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Caputo–Hadamard Fractional Derivatives of Variable Order [PDF]
Numerical Functional Analysis and Optimization, 2016 In this paper we present three types of Caputo-Hadamard derivatives of variable fractional order, and study the relations between them. An approximation formula for each fractional operator, using integer-order derivatives only, is obtained, and an estimation for the error is given.
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Necessary and sufficient conditions for the fractional calculus of variations with Caputo derivatives [PDF]
Commun. Nonlinear Sci. Numer. Simulat. 16 (2011), no. 3,
1490--1500, 2010 We prove optimality conditions for different variational functionals containing left and right Caputo fractional derivatives. A sufficient condition of minimization under an appropriate convexity assumption is given.
Agrawal +31 more
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A Fractional Equation with Left-Sided Fractional Bessel Derivatives of Gerasimov–Caputo Type [PDF]
Mathematics, (2019) Vol. 7, No 12, pp. 1-21, 2019 In the article we propose and study a method to solve ordinary differential equations with left-sided fractional Bessel derivatives on semi-axes of Gerasimov-Caputo type. We derive explicit solutions to equations with fractional powers of Bessel operator using the Meijer integral transform.
Elina Shishkina, С. М. Ситник
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Operator theoretic approach to the Caputo derivative and the fractional diffusion equations [PDF]
arXiv, 2014 The Caputo time-derivative is usually defined pointwise for well-behaved functions, say, for continuously differentiable functions. Accordingly, in the theory of the partial fractional differential equations with the Caputo derivatives, the functional spaces where the solutions are looked for are often the spaces of the smooth functions that are too ...
Rudolf Gorenflo +2 more
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Numerical solutions of fractional optimal control with Caputo–Katugampola derivative
Advances in Difference Equations, 2021 In this paper, we present a numerical technique for solving fractional optimal control problems with a fractional derivative called Caputo–Katugampola derivative. This derivative is a generalization of the Caputo fractional derivative.
N. H. Sweilam +2 more
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AIMS Mathematics, 2022 In this paper, the solutions of some typical nonlinear fractional differential equations are discussed, and the implicit analytical solutions are obtained.
Zhoujin Cui
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Unexpected behavior of Caputo fractional derivative [PDF]
Computational and Applied Mathematics, 2016 This paper discusses the modeling via mathematical methods based on fractional calculus, using Caputo fractional derivative. From the fractional models associated with harmonic oscillator, logistic equation and Malthusian growth, an unexpected behavior of the Caputo fractional derivative is discussed.
Kuroda, Lucas Kenjy Bazaglia +5 more
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