Zobrazeno 1 - 10
of 29
pro vyhledávání: '"26A33, 49K05"'
Publikováno v:
Results in Control and Optimization 14 (2024), Art. 100356, 5 pp
Using the recent weighted generalized fractional order operators of Hattaf, a general fractional optimal control problem without constraints on the values of the control functions is formulated and a corresponding (weak) version of Pontryagin's maxim
Externí odkaz:
http://arxiv.org/abs/2312.10086
In this paper, we derive sufficient conditions ensuring the existence of a weak solution $u$ for a tempered fractional Euler-Lagrange equations $$ \frac{\partial L}{\partial x}(u,{^C}\mathbb{D}_{a^+}^{\alpha, \sigma} u, t) + \mathbb{D}_{b^-}^{\alpha,
Externí odkaz:
http://arxiv.org/abs/2312.06341
Publikováno v:
Axioms 11 (2022), no. 4, Art. 178, 10pp
Integration by parts plays a crucial role in mathematical analysis, e.g., during the proof of necessary optimality conditions in the calculus of variations and optimal control. Motivated by this fact, we construct a new, right-weighted generalized fr
Externí odkaz:
http://arxiv.org/abs/2204.07659
Autor:
Zine, Houssine, Torres, Delfim F. M.
Publikováno v:
Fractal Fract. 2020, 4(3), Art. 38, 11 pp
We introduce a stochastic fractional calculus. As an application, we present a stochastic fractional calculus of variations, which generalizes the fractional calculus of variations to stochastic processes. A stochastic fractional Euler-Lagrange equat
Externí odkaz:
http://arxiv.org/abs/2008.00233
Publikováno v:
Chaos, Solitons & Fractals 102 (2017), 295--304
We introduce an efficient algorithm for computing fractional integrals and derivatives and apply it for solving problems of the calculus of variations of fractional order. The proposed approximations are particularly useful for solving fractional bou
Externí odkaz:
http://arxiv.org/abs/1704.05690
Publikováno v:
Chaos, Solitons & Fractals 102 (2017), 94--98
We obtain Euler-Lagrange equations, transversality conditions and a Noether-like theorem for Herglotz-type variational problems with Lagrangians depending on generalized fractional derivatives. As an application, we consider a damped harmonic oscilla
Externí odkaz:
http://arxiv.org/abs/1704.05697
Publikováno v:
Discrete Contin. Dyn. Syst. Ser. S 11 (2018), no. 1, 59--76
We prove necessary optimality conditions of Pontryagin type for a class of fuzzy fractional optimal control problems with the fuzzy fractional derivative described in the Caputo sense. The new results are illustrated by computing the extremals of thr
Externí odkaz:
http://arxiv.org/abs/1702.01093
Publikováno v:
J. Optim. Theory Appl. 174 (2017), no. 1, 156--175
We develop a simple and accurate method to solve fractional variational and fractional optimal control problems with dependence on Caputo and Riemann-Liouville operators. Using known formulas for computing fractional derivatives of polynomials, we re
Externí odkaz:
http://arxiv.org/abs/1601.06416
Publikováno v:
Math. Meth. Appl. Sci. 38 (2015), no. 9, 1808--1812
In this note we study the application of generalized fractional operators to a particular class of nonstandard Lagrangians. These are typical of dissipative systems and the corresponding Euler-Lagrange and Hamilton equations are analyzed. The depende
Externí odkaz:
http://arxiv.org/abs/1404.6483
Autor:
Odzijewicz, Tatiana
In this PhD thesis we introduce a generalized fractional calculus of variations. We consider variational problems containing generalized fractional integrals and derivatives, and study them using standard (indirect) and direct methods. In particular,
Externí odkaz:
http://arxiv.org/abs/1403.4379