Fractional variational calculus of variable order

Abstract

We study the fundamental problem of the calculus of variations with variable order fractional operators. Fractional integrals are considered in the sense of Riemann-Liouville while derivatives are of Caputo type.

Submitted 26-Sept-2011; accepted 18-Oct-2011; withdrawn by the authors 21-Dec-2011; resubmitted 27-Dec-2011; revised 20-March-2012; accepted 13-April-2012; to 'Advances in Harmonic Analysis and Operator Theory', The Stefan Samko Anniversary Volume (Eds: A. Almeida, L. Castro, F.-O. Speck), Operator Theory: Advances and Applications, Birkhäuser Verlag (http://www.springer.com/series/4850)

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Cited by in corpus (14)

• The Variable-Order Fractional Calculus of Variations
• Caputo derivatives of fractional variable order: numerical approximations
• Optimality Conditions for Fractional Variational Problems with Dependence on a Combined Caputo Derivative of Variable Order
• Noether's theorem for fractional variational problems of variable order
• Combined Fractional Variational Problems of Variable Order and Some Computational Aspects
• Computing Hadamard type operators of variable fractional order
• An expansion formula with higher-order derivatives for fractional operators of variable order
• Constrained fractional variational problems of variable order
• Fractional Herglotz variational problems of variable order
• Variable Order Fractional Variational Calculus for Double Integrals
• A Generalized Fractional Calculus of Variations
• Application of Bernoulli Polynomials for Solving Variable-Order Fractional Optimal Control-Affine Problems
• Numerical Solution of Variable-Order Fractional Differential Equations Using Bernoulli Polynomials
• Complementary Fractional Dimensional Order of Nyquist Sinc Sequences for Time Division Multiplexing