Chapter

Advances in Harmonic Analysis and Operator Theory

Volume 229 of the series Operator Theory: Advances and Applications pp 253-268

Date:

Overview of Fractional h-difference Operators

  • Dorota MozyrskaAffiliated withFaculty of Computer Science, Białystok University of Technology Email author 
  • , Ewa GirejkoAffiliated withFaculty of Computer Science, Białystok University of Technology

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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.

Keywords

Fractional difference operator fractional difference equation fractional derivative.