Leitmann's direct method for fractional optimization problems

Abstract

Based on a method introduced by Leitmann [Internat. J. Non-Linear Mech. {\bf 2} (1967), 55--59], we exhibit exact solutions for some fractional optimization problems of the calculus of variations and optimal control.

Submitted June 16, 2009 and accepted March 15, 2010 for publication in Applied Mathematics and Computation.

References in corpus (12)

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• Fractional conservation laws in optimal control theory
• Calculus of variations with fractional derivatives and fractional integrals
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• Fractional Noether's theorem in the Riesz-Caputo sense
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• Fractional embedding of differential operators and Lagrangian systems
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• Calculus of Variations on Time Scales with Nabla Derivatives
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Cited by in corpus (22)

• Fractional Noether's theorem in the Riesz-Caputo sense
• Fractional Variational Calculus with Classical and Combined Caputo Derivatives
• Fractional calculus of variations for a combined Caputo derivative
• Generalized fractional calculus with applications to the calculus of variations
• Numerical Approximations of Fractional Derivatives with Applications
• Fractional variational problems depending on indefinite integrals
• Discrete Direct Methods in the Fractional Calculus of Variations
• Approximation of fractional integrals by means of derivatives
• Fractional variational calculus for nondifferentiable functions
• A Simple Accurate Method for Solving Fractional Variational and Optimal Control Problems
• Multiobjective fractional variational calculus in terms of a combined Caputo derivative
• Fractional Euler-Lagrange differential equations via Caputo derivatives
• Towards a combined fractional mechanics and quantization
• The power quantum calculus and variational problems
• Hahn's Symmetric Quantum Variational Calculus
• Generalized Transversality Conditions in Fractional Calculus of Variations
• Isoperimetric problems of the calculus of variations with fractional derivatives
• Fractional variational calculus in terms of a combined Caputo derivative
• Mean value theorem for quantum integral operator with application to sharp Ostrowski inequality
• Calculus of Variations with Classical and Fractional Derivatives
• A Discretization Method to Solve Fractional Variational Problems with Dependence on Hadamard Derivatives
• Numerical Approximations to Fractional Problems of the Calculus of Variations and Optimal Control