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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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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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Hartley Series Direct Method for Variational Problems [PDF]
Mathematics Interdisciplinary Research, 2017 The computational method based on using the operational matrix of an orthogonal function for solving variational problems is computer oriented. In this approach, a truncated Hartley series together with the operational matrix of integration and ...
Abbas Saadatmandi
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The Approximation Solution of Some Calculus of Variation Problems Based Euler-Lagrange Equations [PDF]
Engineering and Technology Journal, 2016 The proposed method transforming some of calculus of variation problems into Euler-Lagrange equations, the simplicity and effectiveness of this illustrated through some ...
Zina Khalil Alabacy
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Special Functions of Mathematical Physics: A Unified Lagrangian Formalism
Mathematics, 2020 Lagrangian formalism is established for differential equations with special functions of mathematical physics as solutions. Formalism is based on either standard or non-standard Lagrangians.
Zdzislaw E. Musielak +2 more
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The figuratrix in the calculus of variations [PDF]
Transactions of the American Mathematical Society, 1926 Hadamard defines the figurative of the point (x, y) as the curve F(x', y') 1, where x' and y' are the current co6rdinates, and x and y are considered constant.t The polar reciprocal of the figurative with respect to the unit circle x'2 +y'2 = 1 is termed by Hadamard the figuratrix.
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Hyers-Ulam Stability of Euler’s Equation in the Calculus of Variations
Mathematics, 2021 In this paper we study Hyers-Ulam stability of Euler’s equation in the calculus of variations in two special cases: when F=F(x,y′) and when F=F(y,y′). For the first case we use the direct method and for the second case we use the Laplace transform.
Daniela Marian +2 more
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The Hahn Quantum Variational Calculus [PDF]
Journal of Optimization Theory and Applications, 2010 We introduce the Hahn quantum variational calculus. Necessary and sufficient optimality conditions for the basic, isoperimetric, and Hahn quantum Lagrange problems, are studied. We also show the validity of Leitmann's direct method for the Hahn quantum variational calculus, and give explicit solutions to some concrete problems.
Agnieszka B. Malinowska +1 more
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Variational Principles for Two Compound Nonlinear Equations with Variable Coefficients [PDF]
Journal of Applied and Computational Mechanics, 2021 It is very important to seek explicit variational principles for nonlinear partial differential equations, which are theoretical bases for many methods to solve or analyze the nonlinear phenomena and problems.
Xiao-Qun Cao +4 more
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Basic calculus of variations [PDF]
Pacific Journal of Mathematics, 1983 For the classical one-dimensional problem in the calculus of variations, a necessary condition that the integral be lower semicontinuous is that the integrand be convex as a function of the derivative. We shall see that, if the problem is properly posed, then this condition is also necessary for the ^-dimensional problem.
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