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Fractional Variational Problems Depending on Indefinite Integrals and with Delay

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Abstract

The aim of this paper is to exhibit a necessary and sufficient condition of optimality for functionals depending on fractional integrals and derivatives, on indefinite integrals and on the presence of time delay. We exemplify with one example, where we find analytically the minimizer.

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Acknowledgments

This work was supported by Portuguese funds through the CIDMA - Center for Research and Development in Mathematics and Applications, and the Portuguese Foundation for Science and Technology (FCT-Fundação para a Ciência e a Tecnologia), within Project UID/MAT/04106/2013.

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Authors and Affiliations

  1. CIDMA – Center for Research and Development in Mathematics and Applications, Department of Mathematics, University of Aveiro, Aveiro, Portugal

    Ricardo Almeida

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  1. Ricardo Almeida
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Correspondence to Ricardo Almeida.

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Communicated by Norhashidah M. Ali.

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Almeida, R. Fractional Variational Problems Depending on Indefinite Integrals and with Delay. Bull. Malays. Math. Sci. Soc. 39, 1515–1528 (2016). https://doi.org/10.1007/s40840-015-0248-4

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  • DOI: https://doi.org/10.1007/s40840-015-0248-4

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