Results 21 to 30 of about 924,447 (216)
On Conformable, Riemann-Liouville, and Caputo fractional derivatives [PDF]
, 2022 This article compares conformable fractional Derivative with Riemann-Liouville and Caputo fractional derivative by comparing solutions to fractional ordinary differential equations involving the three fractional derivatives via the numerical simulations ...
Guswanto, Bambang Hendriya +5 more
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Caputo Fractional Derivative and Quantum-Like Coherence [PDF]
Entropy, 2021 We study two forms of anomalous diffusion, one equivalent to replacing the ordinary time derivative of the standard diffusion equation with the Caputo fractional derivative, and the other equivalent to replacing the time independent diffusion coefficient of the standard diffusion equation with a monotonic time dependence.
Garland Culbreth +3 more
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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.
Baleanu, Dumitru, Agrawal, Om. P.
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On Caputo Fractional Derivatives via Convexity [PDF]
Kragujevac Journal of Mathematics, 2020 Summary: In this paper some estimations of Caputo fractional derivatives via convexity have been presented. By using convexity of any positive integer order differentiable function some novel results are given.
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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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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 variational problems depending on indefinite integrals [PDF]
, 2012 We obtain necessary optimality conditions for variational problems with a Lagrangian depending on a Caputo fractional derivative, a fractional and an indefinite integral.
Pooseh, Shakoor +8 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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On Caputo
IEEE Access, 2019 This paper studies the k-fractional analogue of the Caputo fractional derivatives, their properties, and applications. A convolution of two functions instead of the product is analyzed by means of Caputo k-fractional derivatives.
Asif Waheed +5 more
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On a New Modification of the Erdélyi–Kober Fractional Derivative
Fractal and Fractional, 2021 In this paper, we introduce a new Caputo-type modification of the Erdélyi–Kober fractional derivative. We pay attention to how to formulate representations of Erdélyi–Kober fractional integral and derivatives operators.
Zaid Odibat, Dumitru Baleanu
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