MATHEMATICA BOHEMICA, Vol. 135, No. 2, pp. 179-188, 2010

Note on a discretization of a linear fractional differential equation

Jan Cermak, Tomas Kisela

Jan Cermak, Institute of Mathematics, Brno University of Technology, Technicka 2, CZ-616 69 Brno, Czech Republic, e-mail: cermak.j@fme.vutbr.cz; Tomas Kisela, Institute of Mathematics, Brno University of Technology, Technicka 2, CZ-616 69 Brno, Czech Republic, e-mail: kisela.tomas@gmail.com

Abstract: The paper discusses basics of calculus of backward fractional differences and sums. We state their definitions, basic properties and consider a special two-term linear fractional difference equation. We construct a family of functions to obtain its solution.

Keywords: fractional difference, fractional sum, discrete Mittag-Leffler function

Classification (MSC 2010): 39A12, 26A33

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