Results 11 to 20 of about 20,567 (306)
On a Non-Newtonian Calculus of Variations [PDF]
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 \(\mathcal {C}\).
Michel Gondran, Rita Hoblos Saade
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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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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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Problems of stability and well-posedness in the calculus of variations and related PDEs [PDF]
, 2022 We present a collection of three closely related topics regarding the stability and well-posedness of minimization problems in the calculus of variations, namely the generic Tykhonov well-posedness with respect to linear perturbations, the generalized ...
Kalayanamit, Panas
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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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On the foundations of calculus of variations [PDF]
Transactions of the American Mathematical Society, 1941 The subject of this paper will be variational problems fF(x, t)dt = min in parameter form with fixed endpoints. The existence of rectifiable minimizing arcs has been proved under exceedingly general conditions. However, as soon as one wants to establish differentiability properties of the solutions one uses the Euler equations and must therefore assume
Busemann, Herbert, Mayer, Walther
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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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