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Complex-Valued Fractional Derivatives on Time Scales

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Differential and Difference Equations with Applications (ICDDEA 2015)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 164))

Abstract

We introduce a notion of fractional (noninteger order) derivative on an arbitrary nonempty closed subset of the real numbers (on a time scale). Main properties of the new operator are proved and several illustrative examples given.

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References

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Acknowledgements

This research is part of the first author’s Ph.D. project, which is carried out at Sidi Bel Abbes University, Algeria. It was initiated while Bayour was visiting the Department of Mathematics of University of Aveiro, Portugal, 2015. The hospitality of the host institution and the financial support of the University of Chlef, Algeria, are here gratefully acknowledged. Torres was supported by Portuguese funds through CIDMA and FCT, within project UID/MAT/04106/2013.

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Authors and Affiliations

  1. University of Chlef, B.P. 151, Hay Es-salem, Chlef, Algeria

    Benaoumeur Bayour

  2. Department of Mathematics, Center for Research and Development in Mathematics and Applications (CIDMA), University of Aveiro, 3810-193, Aveiro, Portugal

    Delfim F. M. Torres

Authors
  1. Benaoumeur Bayour
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  2. Delfim F. M. Torres
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Corresponding author

Correspondence to Delfim F. M. Torres .

Editor information

Editors and Affiliations

  1. Departamento de Ciências Exactas e Naturais, Academia Militar, Amadora, Portugal

    Sandra Pinelas

  2. Department of Mathematics and Statistics, Masaryk University, Brno, Czech Republic

    Zuzana Došlá

  3. Department of Mathematics and Statistics, Masaryk University, Brno, Czech Republic

    Ondřej Došlý

  4. School of Mathematics and Stastistics, Huazhong University of Science and Technology, Wuhan, China

    Peter E. Kloeden

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Bayour, B., Torres, D.F.M. (2016). Complex-Valued Fractional Derivatives on Time Scales. In: Pinelas, S., Došlá, Z., Došlý, O., Kloeden, P. (eds) Differential and Difference Equations with Applications. ICDDEA 2015. Springer Proceedings in Mathematics & Statistics, vol 164. Springer, Cham. https://doi.org/10.1007/978-3-319-32857-7_8

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