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Národní úložiště šedé literatury Nalezeno 2 záznamů.  Hledání trvalo 0.01 vteřin. 
Basics of Qualitative Theory of Linear Fractional Difference Equations
 Kisela, Tomáš ; Jaroš, Jaroslav (oponent) ; Řehák, Pavel (oponent) ; Čermák, Jan (vedoucí práce)
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.
Úplný záznam
Basics of Qualitative Theory of Linear Fractional Difference Equations
 Kisela, Tomáš ; Jaroš, Jaroslav (oponent) ; Řehák, Pavel (oponent) ; Čermák, Jan (vedoucí práce)
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.
Úplný záznam

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