A Hilbert Space Approach to Fractional Difference Equations

被引：0

作者：

Pham The Anh ^{[1
]}

Babiarz, Artur ^{[2
]}

Czornik, Adam ^{[2
]}

Kitzing, Konrad ^{[3
]}

Niezabitowski, Michal ^{[2
]}

Siegmund, Stefan ^{[3
]}

Trostorff, Sascha ^{[3
]}

Hoang The Tuan ^{[4
]}

机构：

[1] Le Quy Don Tech Univ, Dept Math, 236 Hoang Quoc Viet, Hanoi, Vietnam

[2] Silesian Tech Univ, Fac Automat Control Elect & Comp Sci, Akad 16, PL-44100 Gliwice, Poland

[3] Christian Albrechts Univ Kiel, Math Seminar, Ludewig Meyn Str 4, D-24118 Kiel, Germany

[4] Vietnam Acad Sci & Technol, Inst Math, 18 Hoang Quoc Viet Rd, Hanoi, Vietnam

来源：

DIFFERENCE EQUATIONS AND DISCRETE DYNAMICAL SYSTEMS WITH APPLICATIONS, ICDEA 2018 | 2020年 / 312卷

关键词：

Computational geometry; Graph theory; Hamilton cycles; STABILITY;

D O I：

10.1007/978-3-030-35502-9_4

中图分类号：

Q [生物科学];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

We formulate fractional difference equations of Riemann-Liouville and Caputo type in a functional analytical framework. Main results are existence of solutions on Hilbert space-valued weighted sequence spaces and a condition for stability of linear fractional difference equations. Using a functional calculus, we relate the fractional sum to fractional powers of the operator 1 - tau(-1) with the right shift tau(-1) on weighted sequence spaces. Causality of the solution operator plays a crucial role for the description of initial value problems.

引用

页码：115 / 131

页数：17

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