Generalizing the variational theory on time scales to include the delta indefinite integral

DOI10.1016/j.camwa.2011.02.022zbMath1221.49040arXiv1102.3727OpenAlexW1971748758WikidataQ57651031 ScholiaQ57651031MaRDI QIDQ639047

Delfim F. M. Torres, Natália Martins

Publication date: 18 September 2011

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1102.3727

zbMATH Keywords

Euler-Lagrange equationstime scalescalculus of variationsisoperimetric problemsnatural boundary conditions

Mathematics Subject Classification ID

Fractional ordinary differential equations (34A08) Optimality conditions for problems involving relations other than differential equations (49K21)

Related Items (15)

General fractional variational problem depending on indefinite integrals ⋮ Time scale differential, integral, and variational embeddings of Lagrangian systems ⋮ First order conditions for generalized variational problems over time scales ⋮ A new operational approach for solving fractional variational problems depending on indefinite integrals ⋮ A generalized fractional variational problem depending on indefinite integrals: Euler–Lagrange equation and numerical solution ⋮ Existence of three positive solutions to some \(p\)-Laplacian boundary value problems ⋮ Fractional variational problems depending on indefinite integrals ⋮ Fractional variational problems depending on indefinite integrals and with delay ⋮ Generalized transversality conditions for the Hahn quantum variational calculus ⋮ Noether theorem for non-conservative systems with time delay on time scales ⋮ The existence of solutions for dynamic inclusions on time scales via duality ⋮ The second Noether theorem on time scales ⋮ Nondifferentiable variational principles in terms of a quantum operator ⋮ Variational problems for Hölderian functions with free terminal point ⋮ Parameter-dependent integral on time scales

Cites Work

• Unnamed Item
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• Calculus of variations on time scales with nabla derivatives
• The second Euler-Lagrange equation of variational calculus on time scales
• Noether's symmetry theorem for nabla problems of the calculus of variations
• Leitmann's direct method of optimization for absolute extrema of certain problems of the calculus of variations on time scales
• The Hahn quantum variational calculus
• Transversality conditions for infinite horizon variational problems on time scales
• A general backwards calculus of variations via duality
• Higher-order Hahn's quantum variational calculus
• A unified view of ostensibly disparate isoperimetric variational problems
• Generalizing variational theory to include the indefinite integral, higher derivatives, and a variety of means as cost variables
• Isoperimetric problems in the variational calculus of Euler and Lagrange
• Sturm-Liouville eigenvalue problems on time scales
• The calculus of variations
• An application of time scales to economics
• Inequalities on Time Scales: A Survey
• Isoperimetric Problems on Time Scales with Nabla Derivatives
• Isoperimetric Problems of the Calculus of Variations on Time Scales
• Backward linear control systems on time scales
• The contingent epiderivative and the calculus of variations on time scales
• Integral inequalities and their applications to the calculus of variations on Time Scales
• Quantum calculus

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