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Fractional Variational Calculus for Non-differentiable Functions

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Fractional Dynamics and Control

Abstract

The fractional calculus of variations is a subject under strong research. Different definitions for fractional derivatives and integrals are used, depending on the purpose under study. The fractional operators in this paper are defined in the sense of Jumarie. This allows us to work with functions which are non-differentiable. We present necessary and sufficient optimality conditions for fractional problems of the calculus of variations with a Lagrangian density depending on the free end-points.

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Acknowledgements

This work is partially supported by the Portuguese Foundation for Science and Technology (FCT) through the Systems and Control Group of the R&D Unit CIDMA, and partially by BUT Grant S/WI/2/2011. The author is grateful to Delfim F. M. Torres for inspiring discussions and useful comments.

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Authors and Affiliations

  1. Faculty of Computer Science, Białystok University of Technology, 15-351, Białystok, Poland

    Agnieszka B. Malinowska

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  1. Agnieszka B. Malinowska
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Correspondence to Agnieszka B. Malinowska .

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Editors and Affiliations

  1. Faculty of Art and Sciences, Mathematics and Computer Sciences, Cankaya University, Ankara, Turkey

    Dumitru Baleanu

  2. Institute of Engineering, Department of Electrical Engineering, Polytechnic Institute of Porto, Rua Dr António Bernadino Almeida 431, Porto, 4200-072, Portugal

    José António Tenreiro Machado

  3. Edwardsville, School of Engineering, Southern Illinois University, Room: EB2064, Edwardsville, 62026-1805, USA

    Albert C. J. Luo

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Malinowska, A.B. (2012). Fractional Variational Calculus for Non-differentiable Functions. In: Baleanu, D., Machado, J., Luo, A. (eds) Fractional Dynamics and Control. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-0457-6_8

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  • DOI: https://doi.org/10.1007/978-1-4614-0457-6_8

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  • Print ISBN: 978-1-4614-0456-9

  • Online ISBN: 978-1-4614-0457-6

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