Numerical Solutions of Fractional Differential Equations Arising in Engineering Sciences
This paper deals with the numerical solutions of a class of fractional mathematical models arising in engineering sciences governed by time-fractional advection-diffusion-reaction (TF−ADR) equations, involving the Caputo derivative. In particular, we are interested in the models that link...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-02-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/8/2/215 |
| _version_ | 1819044920312201216 |
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| author | Alessandra Jannelli |
| author_facet | Alessandra Jannelli |
| author_sort | Alessandra Jannelli |
| collection | DOAJ |
| description | This paper deals with the numerical solutions of a class of fractional mathematical models arising in engineering sciences governed by time-fractional advection-diffusion-reaction (TF−ADR) equations, involving the Caputo derivative. In particular, we are interested in the models that link chemical and hydrodynamic processes. The aim of this paper is to propose a simple and robust implicit unconditionally stable finite difference method for solving the TF−ADR equations. The numerical results show that the proposed method is efficient, reliable and easy to implement from a computational viewpoint and can be employed for engineering sciences problems. |
| first_indexed | 2024-12-21T10:20:20Z |
| format | Article |
| id | doaj.art-61723d291af047db8c727eac1bcc7746 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-12-21T10:20:20Z |
| publishDate | 2020-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-61723d291af047db8c727eac1bcc77462022-12-21T19:07:28ZengMDPI AGMathematics2227-73902020-02-018221510.3390/math8020215math8020215Numerical Solutions of Fractional Differential Equations Arising in Engineering SciencesAlessandra Jannelli0Department of Mathematical and Computer Sciences, Physical Sciences and Earth Sciences, University of Messina, Viale F. Stagno d’Alcontres 31, 98166 Messina, ItalyThis paper deals with the numerical solutions of a class of fractional mathematical models arising in engineering sciences governed by time-fractional advection-diffusion-reaction (TF−ADR) equations, involving the Caputo derivative. In particular, we are interested in the models that link chemical and hydrodynamic processes. The aim of this paper is to propose a simple and robust implicit unconditionally stable finite difference method for solving the TF−ADR equations. The numerical results show that the proposed method is efficient, reliable and easy to implement from a computational viewpoint and can be employed for engineering sciences problems.https://www.mdpi.com/2227-7390/8/2/215fractional advection-diffusion-reaction equationcaputo fractional derivativeunconditionally stable finite difference methoddynamics in packed bed column |
| spellingShingle | Alessandra Jannelli Numerical Solutions of Fractional Differential Equations Arising in Engineering Sciences Mathematics fractional advection-diffusion-reaction equation caputo fractional derivative unconditionally stable finite difference method dynamics in packed bed column |
| title | Numerical Solutions of Fractional Differential Equations Arising in Engineering Sciences |
| title_full | Numerical Solutions of Fractional Differential Equations Arising in Engineering Sciences |
| title_fullStr | Numerical Solutions of Fractional Differential Equations Arising in Engineering Sciences |
| title_full_unstemmed | Numerical Solutions of Fractional Differential Equations Arising in Engineering Sciences |
| title_short | Numerical Solutions of Fractional Differential Equations Arising in Engineering Sciences |
| title_sort | numerical solutions of fractional differential equations arising in engineering sciences |
| topic | fractional advection-diffusion-reaction equation caputo fractional derivative unconditionally stable finite difference method dynamics in packed bed column |
| url | https://www.mdpi.com/2227-7390/8/2/215 |
| work_keys_str_mv | AT alessandrajannelli numericalsolutionsoffractionaldifferentialequationsarisinginengineeringsciences |