Relevant bibliographies by topics / Fractional Hamilton-Jacobi equation

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Academic literature on the topic 'Fractional Hamilton-Jacobi equation'

Author: Grafiati
Published: 11 March 2023

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Journal articles on the topic "Fractional Hamilton-Jacobi equation"

1

Jarabah, Ola A. "Quantization of Damped Systems Using Fractional WKB Approximation." Applied Physics Research 10, no. 5 (September 27, 2018): 34. http://dx.doi.org/10.5539/apr.v10n5p34.

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The Hamilton Jacobi theory is used to obtain the fractional Hamilton-Jacobi function for fractional damped systems. The technique of separation of variables is applied here to solve the Hamilton Jacobi partial differential equation for fractional damped systems. The fractional Hamilton-Jacobi function is used to construct the wave function and then to quantize these systems using fractional WKB approximation. The solution of the illustrative example is found to be in exact agreement with the usual classical mechanics for regular Lagrangian when fractional derivatives are replaced with the integer order derivatives and r-0 .
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2

Veretennikova, M., and V. Kolokoltsov. "The Fractional Hamilton-Jacobi-Bellman Equation." Journal of Applied Nonlinear Dynamics 1, no. 1 (March 2017): 45–56. http://dx.doi.org/10.5890/jand.2017.03.004.

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3

Dlotko, Tomasz, and Maria B. Kania. "Subcritical Hamilton-Jacobi fractional equation in RN." Mathematical Methods in the Applied Sciences 38, no. 12 (August 18, 2014): 2547–60. http://dx.doi.org/10.1002/mma.3241.

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4

Gomoyunov, Mikhail Igorevich. "Minimax solutions of Hamilton–Jacobi equations with fractional coinvariant derivatives." ESAIM: Control, Optimisation and Calculus of Variations 28 (2022): 23. http://dx.doi.org/10.1051/cocv/2022017.

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We consider a Cauchy problem for a Hamilton–Jacobi equation with coinvariant derivatives of an order α ∈ (0, 1). Such problems arise naturally in optimal control problems for dynamical systems which evolution is described by differential equations with the Caputo fractional derivatives of the order α. We propose a notion of a generalized in the minimax sense solution of the considered problem. We prove that a minimax solution exists, is unique, and is consistent with a classical solution of this problem. In particular, we give a special attention to the proof of a comparison principle, which requires construction of a suitable Lyapunov–Krasovskii functional.
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5

Hoang Luc, Nguyen, Donal O’Regan, and Anh Tuan Nguyen. "Solutions of a Nonlinear Diffusion Equation with a Regularized Hyper-Bessel Operator." Fractal and Fractional 6, no. 9 (September 19, 2022): 530. http://dx.doi.org/10.3390/fractalfract6090530.

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We investigate the Cauchy problem for a nonlinear fractional diffusion equation, which is modified using the time-fractional hyper-Bessel derivative. The source function is a gradient source of Hamilton–Jacobi type. The main objective of our current work is to show the existence and uniqueness of mild solutions. Our desired goal is achieved using the Picard iteration method, and our analysis is based on properties of Mittag–Leffler functions and embeddings between Hilbert scales spaces and Lebesgue spaces.
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6

Jumarie, Guy. "Fractional Hamilton-Jacobi equation for the optimal control of nonrandom fractional dynamics with fractional cost function." Journal of Applied Mathematics and Computing 23, no. 1-2 (January 2007): 215–28. http://dx.doi.org/10.1007/bf02831970.

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7

Rakhshan, Seyed Ali, Sohrab Effati, and Ali Vahidian Kamyad. "Solving a class of fractional optimal control problems by the Hamilton–Jacobi–Bellman equation." Journal of Vibration and Control 24, no. 9 (September 14, 2016): 1741–56. http://dx.doi.org/10.1177/1077546316668467.

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The performance index of both the state and control variables with a constrained dynamic optimization problem of a fractional order system with fixed final Time have been considered here. This paper presents a general formulation and solution scheme of a class of fractional optimal control problems. The method is based upon finding the numerical solution of the Hamilton–Jacobi–Bellman equation, corresponding to this problem, by the Legendre–Gauss collocation method. The main reason for using this technique is its efficiency and simple application. Also, in this work, we use the fractional derivative in the Riemann–Liouville sense and explain our method for a fractional derivative of order of [Formula: see text]. Numerical examples are provided to show the effectiveness of the formulation and solution scheme.
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8

Gomoyunov, Mikhail I. "Differential Games for Fractional-Order Systems: Hamilton–Jacobi–Bellman–Isaacs Equation and Optimal Feedback Strategies." Mathematics 9, no. 14 (July 15, 2021): 1667. http://dx.doi.org/10.3390/math9141667.

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The paper deals with a two-person zero-sum differential game for a dynamical system described by differential equations with the Caputo fractional derivatives of an order α∈(0,1) and a Bolza-type cost functional. A relationship between the differential game and the Cauchy problem for the corresponding Hamilton–Jacobi–Bellman–Isaacs equation with fractional coinvariant derivatives of the order α and the natural boundary condition is established. An emphasis is given to construction of optimal positional (feedback) strategies of the players. First, a smooth case is studied when the considered Cauchy problem is assumed to have a sufficiently smooth solution. After that, to cope with a general non-smooth case, a generalized minimax solution of this problem is involved.
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9

YAN, Li. "An Optimal Portfolio Problem Presented by Fractional Brownian Motion and Its Applications." Wuhan University Journal of Natural Sciences 27, no. 1 (March 2022): 53–56. http://dx.doi.org/10.1051/wujns/2022271053.

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We use the dynamic programming principle method to obtain the Hamilton-Jacobi-Bellman (HJB) equation for the value function, and solve the optimal portfolio problem explicitly in a Black-Scholes type of market driven by fractional Brownian motion with Hurst parameter [see formula in PDF]. The results are compared with the corresponding well-known results in the standard Black-Scholes market [see formula in PDF]. As an application of our proposed model, two optimal problems are discussed and solved, analytically.
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10

Silvestre, Luis. "On the differentiability of the solution to the Hamilton–Jacobi equation with critical fractional diffusion." Advances in Mathematics 226, no. 2 (January 2011): 2020–39. http://dx.doi.org/10.1016/j.aim.2010.09.007.

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Book chapters on the topic "Fractional Hamilton-Jacobi equation"

1

"10 Dirichlet’s problem for critical Hamilton–Jacobi fractional equation." In Critical Parabolic-Type Problems, 231–54. De Gruyter, 2020. http://dx.doi.org/10.1515/9783110599831-010.

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2

Dłotko, Tomasz W., and Yejuan Wang. "Erratum to: Chapter 10 Dirichlet’s problem for critical Hamilton-Jacobi fractional equation." In Critical Parabolic-Type Problems, 297–300. De Gruyter, 2020. http://dx.doi.org/10.1515/9783110599831-017.

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