Results 1 to 10 of about 13,733 (253)
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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Oberwolfach Reports, 2013 The calculus of variations is a branch of mathematical analysis that studies extrema and critical points of functionals (or energies).
George B. Arfken +2 more
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Riemannian Calculus of Variations Using Strongly Typed Tensor Calculus
Mathematics, 2022 In this paper, the notion of strongly typed language will be borrowed from the field of computer programming to introduce a calculational framework for linear algebra and tensor calculus for the purpose of detecting errors resulting from inherent misuse ...
Victor Dods
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On a Non-Newtonian Calculus of Variations
Axioms, 2021 The calculus of variations is a field of mathematical analysis born in 1687 with Newton’s problem of minimal resistance, which is concerned with the maxima or minima of integral functionals.
Delfim F. M. Torres
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Complex Calculus of Variations [PDF]
IFAC Proceedings Volumes, 2001 Summary: In this article we present a detailed study of the complex calculus of variations introduced in \textit{M. Gondran} [C. R. Acad. Sci., Paris, Sér. I, Math. 332, No. 7, 677--680 (2001; Zbl 1007.49014)]. This calculus is analogous to the conventional calculus of variations, but is applied here to \(\mathcal {C}^n\) functions in \(\mathcal {C}\).
Gondran, Michel, Saade, Rita Hoblos
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Oberwolfach Reports, 2005 The workshop continued the longstanding biannual series at Oberwolfach on Calculus of Variations. This Oberwolfach series provides an imporant service to the mathematics community, being currently the only periodic international meeting in this very active area.
Gianni Dal Maso +2 more
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A Stochastic Fractional Calculus with Applications to Variational Principles
Fractal and Fractional, 2020 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.
Houssine Zine, Delfim F. M. Torres
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Symmetric Divergence-free tensors in the Calculus of Variations
Comptes Rendus. Mathématique, 2022 Divergence-free symmetric tensors seem ubiquitous in Mathematical Physics. We show that this structure occurs in models that are described by the so-called “second” variational principle, where the argument of the Lagrangian is a closed differential form.
Serre, Denis
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The variational calculus on time scales [PDF]
International Journal for Simulation and Multidisciplinary Design Optimization, 2010 The discrete, the quantum, and the continuous calculus of variations, have been recently unified and extended by using the theory of time scales. Such unification and extension is, however, not unique, and two approaches are followed in the literature ...
Torrest Delfim F.M.
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