A normalized Caputo–Fabrizio fractional diffusion equation
We propose a normalized Caputo–Fabrizio (CF) fractional diffusion equation. The CF fractional derivative replaces the power-law kernel in the Caputo derivative with an exponential kernel, which avoids singularities. Compared to the Caputo derivative, the CF derivative is better suited for systems wh...
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| Language: | English |
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AIMS Press
2025-03-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2025282 |
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| author | Junseok Kim |
| author_facet | Junseok Kim |
| author_sort | Junseok Kim |
| collection | DOAJ |
| description | We propose a normalized Caputo–Fabrizio (CF) fractional diffusion equation. The CF fractional derivative replaces the power-law kernel in the Caputo derivative with an exponential kernel, which avoids singularities. Compared to the Caputo derivative, the CF derivative is better suited for systems where memory effects decay smoothly rather than following a power law. However, the kernel is not normalized in the sense that its weighting function does not integrate to unity. To resolve this limitation, we develop a modified formulation that ensures proper normalization. To investigate the fractional order's effect on evolution dynamics, we perform computational tests that highlight memory effects. |
| format | Article |
| id | doaj-art-7986011477694f1ea2a6bd7e657d8dff |
| institution | OA Journals |
| issn | 2473-6988 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj-art-7986011477694f1ea2a6bd7e657d8dff2025-08-20T02:08:20ZengAIMS PressAIMS Mathematics2473-69882025-03-011036195620810.3934/math.2025282A normalized Caputo–Fabrizio fractional diffusion equationJunseok Kim0Department of Mathematics, Korea University, Seoul 02841, Republic of KoreaWe propose a normalized Caputo–Fabrizio (CF) fractional diffusion equation. The CF fractional derivative replaces the power-law kernel in the Caputo derivative with an exponential kernel, which avoids singularities. Compared to the Caputo derivative, the CF derivative is better suited for systems where memory effects decay smoothly rather than following a power law. However, the kernel is not normalized in the sense that its weighting function does not integrate to unity. To resolve this limitation, we develop a modified formulation that ensures proper normalization. To investigate the fractional order's effect on evolution dynamics, we perform computational tests that highlight memory effects.https://www.aimspress.com/article/doi/10.3934/math.2025282normalized caputo–fabrizio fractional derivativecaputo derivativediffusion equation |
| spellingShingle | Junseok Kim A normalized Caputo–Fabrizio fractional diffusion equation AIMS Mathematics normalized caputo–fabrizio fractional derivative caputo derivative diffusion equation |
| title | A normalized Caputo–Fabrizio fractional diffusion equation |
| title_full | A normalized Caputo–Fabrizio fractional diffusion equation |
| title_fullStr | A normalized Caputo–Fabrizio fractional diffusion equation |
| title_full_unstemmed | A normalized Caputo–Fabrizio fractional diffusion equation |
| title_short | A normalized Caputo–Fabrizio fractional diffusion equation |
| title_sort | normalized caputo fabrizio fractional diffusion equation |
| topic | normalized caputo–fabrizio fractional derivative caputo derivative diffusion equation |
| url | https://www.aimspress.com/article/doi/10.3934/math.2025282 |
| work_keys_str_mv | AT junseokkim anormalizedcaputofabriziofractionaldiffusionequation AT junseokkim normalizedcaputofabriziofractionaldiffusionequation |