Results 21 to 30 of about 20,179 (274)
Necessary optimality conditions for fractional difference problems of the calculus of variations
Discrete & Continuous Dynamical Systems - A, 2011 We introduce a discrete-time fractional calculus of variations. First and second order necessary optimality conditions are established. Examples illustrating the use of the new Euler-Lagrange and Legendre type conditions are given. They show that the solutions of the fractional problems coincide with the solutions of the corresponding non-fractional ...
Bastos, N.R.O. +2 more
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Fractional Damping Through Restricted Calculus of Variations [PDF]
Journal of Nonlinear Science, 2021 Key words and phrases: Continuous/discrete Lagrangian and Hamiltonian modelling, fractional derivatives, fractional dissipative systems, fractional differential equations, variational principles, variational integrators. 30 pages, 7 figures. Constructive comments are welcome!!
Jiménez, Fernando, Ober-Blöbaum, Sina
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Minimization Problems for Functionals Depending on Generalized Proportional Fractional Derivatives
Fractal and Fractional, 2022 In this work we study variational problems, where ordinary derivatives are replaced by a generalized proportional fractional derivative. This fractional operator depends on a fixed parameter, acting as a weight over the state function and its first-order
Ricardo Almeida
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Euler–Lagrange-Type Equations for Functionals Involving Fractional Operators and Antiderivatives
Mathematics, 2023 The goal of this paper is to present the necessary and sufficient conditions that every extremizer of a given class of functionals, defined on the set C1[a,b], must satisfy.
Ricardo Almeida
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Optimal State Control of Fractional Order Differential Systems: The Infinite State Approach
Fractal and Fractional, 2021 Optimal control of fractional order systems is a long established domain of fractional calculus. Nevertheless, it relies on equations expressed in terms of pseudo-state variables which raise fundamental questions.
Jean-Claude Trigeassou, Nezha Maamri
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Fractal and Fractional, 2023 In this paper, we investigate the necessary conditions to optimize a given functional, involving a generalization of the tempered fractional derivative.
Ricardo Almeida
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Modified Mittag-Leffler Functions with Applications in Complex Formulae for Fractional Calculus
Fractal and Fractional, 2020 Mittag-Leffler functions and their variations are a popular topic of study at the present time, mostly due to their applications in fractional calculus and fractional differential equations.
Arran Fernandez, Iftikhar Husain
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Fractional calculus of variations of several independent variables [PDF]
The European Physical Journal Special Topics, 2013 We prove multidimensional integration by parts formulas for generalized fractional derivatives and integrals. The new results allow us to obtain optimality conditions for multidimensional fractional variational problems with Lagrangians depending on generalized partial integrals and derivatives. A generalized fractional Noether's theorem, a formulation
Odzijewicz, Tatiana +2 more
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Fractal and Fractional, 2022 In this paper, we consider Herglotz-type variational problems dealing with fractional derivatives of distributed-order with respect to another function.
Fátima Cruz +2 more
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Further Research for Lagrangian Mechanics within Generalized Fractional Operators
Fractal and Fractional, 2023 In this article, the problems of the fractional calculus of variations are discussed based on generalized fractional operators, and the corresponding Lagrange equations are established.
Chuanjing Song
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