Overview of fractional \(h\)-difference operators. (English) Zbl 1262.39024
Almeida, Alexandre (ed.) et al., Advances in harmonic analysis and operator theory. The Stefan Samko anniversary volume on the occasion of his 70th birthday. Mainly based on the presentations at two conferences, Lisbon and Aveiro, Portugal, in June – July, 2011. Basel: Birkhäuser (ISBN 978-3-0348-0515-5/hbk; 978-3-0348-0516-2/ebook). Operator Theory: Advances and Applications 229, 253-268 (2013).
Summary: 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.
For the entire collection see [Zbl 1258.00012].
For the entire collection see [Zbl 1258.00012].
