Publication detail

Basics of Qualitative Theory of Linear Fractional Difference Equations

KISELA, T.

Original Title

Basics of Qualitative Theory of Linear Fractional Difference Equations

Type

dissertation

Language

English

Original Abstract

This doctoral thesis concerns with the fractional calculus on discrete settings, namely in the frame of the so-called (q,h)-calculus and its special case h-calculus. First, foundations of the theory of linear fractional difference equations in (q,h)-calculus are established. In particular, basic properties, such as existence, uniqueness and structure of solutions, are discussed and a discrete analogue of the Mittag-Leffler function is introduced via eigenfunctions of a fractional difference operator. Further, qualitative analysis of a scalar and vector test fractional difference equation is performed in the frame of h-calculus. The results of stability and asymptotic analysis enable us to specify the connection to other mathematical disciplines, such as continuous fractional calculus, Volterra difference equations and numerical analysis. Finally, a possible generalization of the fractional calculus to more general settings is outlined.

Keywords

fractional calculus -- time scales -- fractional difference equation -- Riemann-Liouville difference operator -- stability -- asymptotic behaviour -- discrete Mittag-Leffler function -- Volterra difference equation -- Laplace transform

Authors

KISELA, T.

Released

28. 8. 2012

Pages count

69

BibTex

@phdthesis{BUT94958,
  author="Tomáš {Kisela}",
  title="Basics of Qualitative Theory of Linear Fractional Difference Equations",
  pages="69",
  year="2012"
}