Exact solutions of fractional oscillator eigenfunction problem with fixed memory length

• Autorzy: Klimek Malgorzata , Blaszczyk Tomasz

Identyfikatory

DOI

10.17512/jamcm.2024.1.04

• Języki publikacji: EN

Abstrakty

EN

In this paper, the eigenproblem for a fractional oscillator under homogeneous Dirichlet and Neumann boundary conditions is considered. Key properties of fractional operators with fixed memory length are established, such as the connection between left and right operators, the product rule for fractional integrals, and the fractional integration by the parts rule for periodic/antiperiodic functions. Explicit solutions in the form of discrete sets of sine/cosine eigenfunctions are derived. The impact of fractional order and memory length on eigenvalues is presented on graphs. Finally, a comparison of eigenvalues of oscillator with a fixed memory length and infinite memory length is shown.

Słowa kluczowe

EN

eigenproblem; fractional operators; fixed memory length

PL

operatory ułamkowe; całki; funkcja okresowa; warunek Dirichleta

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Journal of Applied Mathematics and Computational Mechanics
• Rocznik: 2024
• Tom: Vol. 23, nr 1
• Strony: 45--58
• Opis fizyczny: Bibliogr. 28 poz.

Twórcy

autor

Klimek Malgorzata

• Department of Mathematics, Czestochowa University of Technology Czestochowa, Poland

autor

Blaszczyk Tomasz

• Department of Mathematics, Czestochowa University of Technology Czestochowa, Poland

Bibliografia

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Uwagi

Opracowanie rekordu ze środków MNiSW, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2024).