Applications of the Fractional Sturm–Liouville Difference Problem to the Fractional Diffusion Difference Equation
This paper deals with homogeneous and non-homogeneous fractional diffusion difference equations. The fractional operators in space and time are defined in the sense of Grünwald and Letnikov. Applying results on the existence of eigenvalues and corresponding eigenfunctions of the Sturm–Liouville prob...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Sciendo
2023-09-01
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| Series: | International Journal of Applied Mathematics and Computer Science |
| Subjects: | |
| Online Access: | https://doi.org/10.34768/amcs-2023-0025 |
| _version_ | 1827793325199982592 |
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| author | Malinowska Agnieszka B. Odzijewicz Tatiana Poskrobko Anna |
| author_facet | Malinowska Agnieszka B. Odzijewicz Tatiana Poskrobko Anna |
| author_sort | Malinowska Agnieszka B. |
| collection | DOAJ |
| description | This paper deals with homogeneous and non-homogeneous fractional diffusion difference equations. The fractional operators in space and time are defined in the sense of Grünwald and Letnikov. Applying results on the existence of eigenvalues and corresponding eigenfunctions of the Sturm–Liouville problem, we show that solutions of fractional diffusion difference equations exist and are given by a finite series. |
| first_indexed | 2024-03-11T18:15:53Z |
| format | Article |
| id | doaj.art-29f21b2df8124cd386950e1a082df287 |
| institution | Directory Open Access Journal |
| issn | 2083-8492 |
| language | English |
| last_indexed | 2024-03-11T18:15:53Z |
| publishDate | 2023-09-01 |
| publisher | Sciendo |
| record_format | Article |
| series | International Journal of Applied Mathematics and Computer Science |
| spelling | doaj.art-29f21b2df8124cd386950e1a082df2872023-10-16T06:08:09ZengSciendoInternational Journal of Applied Mathematics and Computer Science2083-84922023-09-0133334935910.34768/amcs-2023-0025Applications of the Fractional Sturm–Liouville Difference Problem to the Fractional Diffusion Difference EquationMalinowska Agnieszka B.0Odzijewicz Tatiana1Poskrobko Anna21Faculty of Computer Science, Bialystok University of Technology, ul. Wiejska 45A, 15-351Białystok, Poland2Institute of Mathematical Economics, SGH Warsaw School of Economics Al. Niepodległości 162, 02-554Warsaw, Poland1Faculty of Computer Science, Bialystok University of Technology, ul. Wiejska 45A, 15-351Białystok, PolandThis paper deals with homogeneous and non-homogeneous fractional diffusion difference equations. The fractional operators in space and time are defined in the sense of Grünwald and Letnikov. Applying results on the existence of eigenvalues and corresponding eigenfunctions of the Sturm–Liouville problem, we show that solutions of fractional diffusion difference equations exist and are given by a finite series.https://doi.org/10.34768/amcs-2023-0025anomalous diffusionfractional diffusion equationsfractional calculusdifference equations |
| spellingShingle | Malinowska Agnieszka B. Odzijewicz Tatiana Poskrobko Anna Applications of the Fractional Sturm–Liouville Difference Problem to the Fractional Diffusion Difference Equation International Journal of Applied Mathematics and Computer Science anomalous diffusion fractional diffusion equations fractional calculus difference equations |
| title | Applications of the Fractional Sturm–Liouville Difference Problem to the Fractional Diffusion Difference Equation |
| title_full | Applications of the Fractional Sturm–Liouville Difference Problem to the Fractional Diffusion Difference Equation |
| title_fullStr | Applications of the Fractional Sturm–Liouville Difference Problem to the Fractional Diffusion Difference Equation |
| title_full_unstemmed | Applications of the Fractional Sturm–Liouville Difference Problem to the Fractional Diffusion Difference Equation |
| title_short | Applications of the Fractional Sturm–Liouville Difference Problem to the Fractional Diffusion Difference Equation |
| title_sort | applications of the fractional sturm liouville difference problem to the fractional diffusion difference equation |
| topic | anomalous diffusion fractional diffusion equations fractional calculus difference equations |
| url | https://doi.org/10.34768/amcs-2023-0025 |
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