Anh, P.T. and Babiarz, A. and Czornik, A. and Kitzing, K. and Niezabitowski, M. and Siegmund, S. and Trostorff, S. and Tuan, H.T. (2020) A Hilbert Space Approach to Fractional Difference Equations. In: 24th International Conference on Difference Equations and Applications, ICDEA 2018, 21 May 2018 through 25 May 2018.
02. A Hilbert Space Approach to Fractional Difference Equations .pdf
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Abstract
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 (Formula Presented) with the right shift (Formula Presented) on weighted sequence spaces. Causality of the solution operator plays a crucial role for the description of initial value problems. © Springer Nature Switzerland AG 2020.
| Item Type: | Conference or Workshop Item (Paper) |
|---|---|
| Divisions: | Faculties > Faculty of Information Technology |
| Identification Number: | 10.1007/978-3-030-35502-9_4 |
| Uncontrolled Keywords: | Calculations; Computation theory; Computational geometry; Dynamical systems; Graph theory; Hilbert spaces; Initial value problems; Vector spaces; Existence of Solutions; Fractional power; Functional calculus; Hamilton cycle; Liouville; Weighted sequences; Difference equations |
| Additional Information: | Conference code: 237299. Language of original document: English. All Open Access, Green. |
| URI: | http://eprints.lqdtu.edu.vn/id/eprint/9164 |
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