共查询到20条相似文献,搜索用时 15 毫秒
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Agnieszka B. Malinowska Delfim F.M. Torres 《Applied mathematics and computation》2012,218(9):5099-5111
The study of fractional variational problems in terms of a combined fractional Caputo derivative is introduced. Necessary optimality conditions of Euler-Lagrange type for the basic, isoperimetric, and Lagrange variational problems are proved, as well as transversality and sufficient optimality conditions. This allows to obtain necessary and sufficient Pareto optimality conditions for multiobjective fractional variational problems. 相似文献
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A. Babakhani Varsha Daftardar-Gejji 《Journal of Mathematical Analysis and Applications》2002,270(1):66-79
Local fractional derivative (LFD) operators have been introduced in the recent literature (Chaos 6 (1996) 505-513). Being local in nature these derivatives have proven useful in studying fractional differentiability properties of highly irregular and nowhere differentiable functions. In the present paper we prove Leibniz rule, chain rule for LFD operators. Generalization of directional LFD and multivariable fractional Taylor series to higher orders have been presented. 相似文献
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Tatiana Odzijewicz 《Nonlinear Analysis: Theory, Methods & Applications》2012,75(3):1507-1515
We give a proper fractional extension of the classical calculus of variations by considering variational functionals with a Lagrangian depending on a combined Caputo fractional derivative and the classical derivative. Euler-Lagrange equations to the basic and isoperimetric problems as well as transversality conditions are proved. 相似文献
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V. I. Arnol'd 《Journal of Mathematical Sciences》1984,27(3):2679-2713
A survey is given of theories of singularities of systems of rays and wave fronts, that is, singularities of systems of extremals of variational problems and solutions of the Hamilton-Jacobi equations near caustics. The problem of passing about an obstacle bounded by a smooth surface of general position is studied in detail. Theorems are proved on the normal forms of Lagrangian manifolds with singularities formed by rays of the system of extremals of a variational problem in the symplectic space of all oriented lines which tear off from the surface of the obstacle as well as theorems on Legendre manifolds with singularities formed by contact elements of a wave front and 1-jets of a solution of the Hamilton-Jacobi equation.Translated from Itogi Nauki i Tekhniki, Seriya Sovremennye Problemy Matematiki, Vol. 22, pp. 3–55, 1983. 相似文献
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George Maltese 《Acta Appl Math》1991,24(3):311-311
Book Review
Convexity methods in variational calculusPeter Smith: (Electronic and Electrical Engineering Research Studies. Applied and Engineering Mathematics Series 1), John Wiley, New York (ISBN 0471 906794), 1985. Research Studies Press, U.K. (ISBN 0 86380 022 X). 相似文献8.
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A. V. Dmitruk 《Mathematical Notes》1976,20(6):1032-1038
The use of the method of the Euler-Jacobi equation is considered in the study of a quadratic functional defined on a cone. Such functionals occur in the variation of optimal-control problems. Several concepts are introduced with the aid of which the Euler-Jacobi equation is extended and the application of this method is justified also in the case that the equation is not a linear differential equation.Translated from Matematicheskie Zametki, Vol. 20, No. 6, pp. 847–858, December, 1976. 相似文献
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Dongling Wang Aiguo Xiao 《Communications in Nonlinear Science & Numerical Simulation》2012,17(2):602-610
In this paper, the fractional variational integrators for a class of fractional variational problems are developed. The fractional discrete Euler-Lagrange equation is obtained. Based on the Grünwald-Letnikov method and Diethelm’s fractional backward differences, some fractional variational integrators are presented and the fractional variational errors are discussed. Some numerical examples are presented to illustrate these results. 相似文献
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《Communications in Nonlinear Science & Numerical Simulation》2011,16(3):1490-1500
We prove optimality conditions for different variational functionals containing left and right Caputo fractional derivatives. A sufficient condition of minimization under an appropriate convexity assumption is given. An Euler–Lagrange equation for functionals where the lower and upper bounds of the integral are distinct of the bounds of the Caputo derivative is also proved. Then, the fractional isoperimetric problem is formulated with an integral constraint also containing Caputo derivatives. Normal and abnormal extremals are considered. 相似文献
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《Communications in Nonlinear Science & Numerical Simulation》2011,16(3):1140-1153
This survey intends to report some of the major documents and events in the area of fractional calculus that took place since 1974 up to the present date. 相似文献
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Dumitru Baleanu 《Communications in Nonlinear Science & Numerical Simulation》2009,14(6):2520-2523
In this paper, a new method of finding the fractional Euler–Lagrange equations within Caputo derivative is proposed by making use of the fractional generalization of the classical Faá di Bruno formula. The fractional Euler–Lagrange and the fractional Hamilton equations are obtained within the 1 + 1 field formalism. One illustrative example is analyzed. 相似文献
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Generalized variational inequalities 总被引:5,自引:0,他引:5
This paper introduces and analyzes generalized variational inequalities. The most general existence theory is established, traditional coercivity conditions are extended, properties of solution sets under various monotonicity conditions are investigated, and a computational scheme is considered. Similar results can be obtained for generalized complementarity and fixed-point problems.The authors are indebted to Professor R. Saigal of Northwestern University for his continuous encouragement and helpful discussions concerning this paper. 相似文献
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John David Logan 《Aequationes Mathematicae》1973,9(2-3):210-220
The intent of this paper is to show that first integrals of the discrete Euler equation can be determined explicitly by investigating the invariance properties of the discrete Lagrangian. The result obtained is a discrete analog of the classical theorem of E. Noether in the Calculus of Variations. 相似文献
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A. P. Grinko 《Integral Transforms and Special Functions》2018,29(6):489-504
Generalized Abel type integral equations with Gauss, Kummer's and Humbert's confluent hypergeometric functions in the kernel and generalized Abel type integral equations with localized fractional integrals are considered. The left-hand sides of these equations are inversed by using generalized fractional derivatives. Explicit solutions of the equations in the class of locally summable functions are obtained. They are represented in terms of hypergeometric functions. Asymptotic power exponential type expansions of the generalized and localized fractional integrals are obtained. The base solutions of the generalized Abel type integral equation are given in the form of asymptotic series. 相似文献
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