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Advances in Harmonic Analysis and Operator Theory pp 253–268Cite as

Birkhäuser

Overview of Fractional h-difference Operators

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Part of the book series: Operator Theory: Advances and Applications ((OT,volume 229))

Abstract

Fractional difference operators and their properties are discussed. We give a characterization of three operators that we call Grünwald-Letnikov, Riemann-Liouville and Caputo like difference operators. We show relations among them. In the paper, linear fractional h-difference equations are described. We give formulas of solutions to initial value problems. Crucial formulas are gathered in the tables presented in the last section of the paper.

Mathematics Subject Classification (2010). Primary 39A70; Secondary 26A33.

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Author information

Authors and Affiliations

  1. Faculty of Computer Science, Białystok University of Technology, Wiejska 45a, PL-15-351, Białystok, Poland

    Dorota Mozyrska & Ewa Girejko

Authors
  1. Dorota Mozyrska
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  2. Ewa Girejko
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Corresponding author

Correspondence to Dorota Mozyrska .

Editor information

Editors and Affiliations

  1. , Departamento de Matemática, Universidade de Aveiro, Campus Universitário de Santiago, Aveiro, 3810-193, Portugal

    Alexandre Almeida

  2. , Departamento de Matemática, Universidade de Aveiro, Campus Universitário de Santiago, Aveiro, 3810-193, Portugal

    Luís Castro

  3. Instituto Superior Tecnico, Depto. Matematica, Universidade Tecnica Lisboa, Av. Rovisco Pais 1, Lisboa, 1049-001, Portugal

    Frank-Olme Speck

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Mozyrska, D., Girejko, E. (2013). Overview of Fractional h-difference Operators. In: Almeida, A., Castro, L., Speck, FO. (eds) Advances in Harmonic Analysis and Operator Theory. Operator Theory: Advances and Applications, vol 229. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0516-2_14

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