Results 11 to 20 of about 6,141 (192)
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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Laplace Variational Iteration Method for Modified Fractional Derivatives with Non-singular Kernel [PDF]
Journal of Applied and Computational Mechanics, 2020 A universal approach by Laplace transform to the variational iteration method for fractional derivatives with the nonsingular kernel is presented; in particular, the Caputo-Fabrizio fractional derivative and the Atangana-Baleanu fractional derivative ...
Huitzilín Yépez-Martínez +1 more
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Mathematics, 2022 The generalized proportional Caputo fractional derivative is a comparatively new type of derivative that is a generalization of the classical Caputo fractional derivative, and it gives more opportunities to adequately model complex phenomena in physics ...
Ravi Agarwal +2 more
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A Nonlinear Implicit Fractional Equation with Caputo Derivative [PDF]
Journal of Mathematics, 2021 In this paper, we study a nonlinear implicit differential equation with initial conditions. The considered problem involves the fractional Caputo derivatives under some conditions on the order. We prove an existence and uniqueness analytic result by application of Banach principle.
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Fractional hamilton formalism within caputo’s derivative [PDF]
Czechoslovak Journal of Physics, 2006 In this paper we develop a fractional Hamiltonian formulation for dynamic systems defined in terms of fractional Caputo derivatives. Expressions for fractional canonical momenta and fractional canonical Hamiltonian are given, and a set of fractional Hamiltonian equations are obtained.
Om P. Agrawal, Dumitru Baleanu
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Exact results for a fractional derivative of elementary functions
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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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
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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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