Results 31 to 40 of about 366,087 (286)
A new Definition of Fractional Derivative and Fractional Integral [PDF]
Kirkuk Journal of Science, 2018 In this paper, we introduce three different definitions of fractional derivatives, namely Riemann-Liouville derivative, Caputo derivative and the new formula Caputo expansion formula, and some basics properties of these derivatives are discussed.
Ahmed M. Kareem
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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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A Caputo fractional derivative-based algorithm for optimization
CoRR, 2021 We propose a novel Caputo fractional derivative-based optimization algorithm. Upon defining the Caputo fractional gradient with respect to the Cartesian coordinate, we present a generic Caputo fractional gradient descent (CFGD) method. We prove that the CFGD yields the steepest descent direction of a locally smoothed objective function.
Yeonjong Shin +2 more
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Boundary Value Problems, 2017 By mixing the idea of 2-arrays, continued fractions, and Caputo-Fabrizio fractional derivative, we introduce a new operator entitled the infinite coefficient-symmetric Caputo-Fabrizio fractional derivative.
Dumitru Baleanu +2 more
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Introduction to the fractional-order chaotic system under fractional operator in Caputo sense
Alexandria Engineering Journal, 2021 In this paper, we consider a new fractional-order chaotic system described by the Caputo fractional derivative. This paper’s main objective is to analyze the bifurcation maps to detect the chaotic regions for a new fractional-order chaotic system.
Ndolane Sene
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Alexandria Engineering Journal, 2023 In this research paper, the third-order fractional partial differential equation (FPDE) in the sense of the Caputo fractional derivative and the Atangana-Baleanu Caputo (ABC) fractional derivative is investigated for the first time. The importance of the
Shorish Omer Abdulla +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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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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Caputo and related fractional derivatives in singular systems [PDF]
Applied Mathematics and Computation, 2018 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Dassios, Ioannis K., Baleanu, Dumitru
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EQUIVALENCE OF INITIALIZED RIEMANN-LIOUVILLE AND CAPUTO DERIVATIVES
Journal of Applied Analysis & Computation, 2020 Summary: Initialization of fractional differential equations remains an ongoing problem. The initialization function approach and the infinite state approach provide two effective ways of dealing with this issue. The purpose of this paper is to prove the equivalence of the initialized Riemann-Liouville derivative and the initialized Caputo derivative ...
Yuan, Jian +3 more
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