Modelling and analysis of fractal-fractional partial differential equations: Application to reaction-diffusion model
In this paper, an extension is paid to an idea of fractal and fractional derivatives which has been applied to a number of ordinary differential equations to model a system of partial differential equations. As a case study, the fractal fractional Schnakenberg system is formulated with the Caputo op...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Elsevier
2020-08-01
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| Series: | Alexandria Engineering Journal |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S1110016820301216 |
| _version_ | 1818907144296071168 |
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| author | Kolade M. Owolabi Abdon Atangana Ali Akgul |
| author_facet | Kolade M. Owolabi Abdon Atangana Ali Akgul |
| author_sort | Kolade M. Owolabi |
| collection | DOAJ |
| description | In this paper, an extension is paid to an idea of fractal and fractional derivatives which has been applied to a number of ordinary differential equations to model a system of partial differential equations. As a case study, the fractal fractional Schnakenberg system is formulated with the Caputo operator (in terms of the power law), the Caputo-Fabrizio operator (with exponential decay law) and the Atangana-Baleanu fractional derivative (based on the Mittag-Liffler law). We design some algorithms for the Schnakenberg model by using the newly proposed numerical methods. In such schemes, it worth mentioning that the classical cases are recovered whenever α=1 and β=1. Numerical results obtained for different fractal-order (β∈(0,1)) and fractional-order (α∈(0,1)) are also given to address any point and query that may arise. |
| first_indexed | 2024-12-19T21:50:27Z |
| format | Article |
| id | doaj.art-bd15304761e94ab2a300df273fa5d466 |
| institution | Directory Open Access Journal |
| issn | 1110-0168 |
| language | English |
| last_indexed | 2024-12-19T21:50:27Z |
| publishDate | 2020-08-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Alexandria Engineering Journal |
| spelling | doaj.art-bd15304761e94ab2a300df273fa5d4662022-12-21T20:04:25ZengElsevierAlexandria Engineering Journal1110-01682020-08-0159424772490Modelling and analysis of fractal-fractional partial differential equations: Application to reaction-diffusion modelKolade M. Owolabi0Abdon Atangana1Ali Akgul2Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Viet Nam; Institute for Groundwater Studies, Faculty of Natural and Agricultural Sciences, University of the Free State, Bloemfontein 9300, South Africa; Corresponding author.Institute for Groundwater Studies, Faculty of Natural and Agricultural Sciences, University of the Free State, Bloemfontein 9300, South AfricaDepartment of Mathematics, Siirt University, TurkeyIn this paper, an extension is paid to an idea of fractal and fractional derivatives which has been applied to a number of ordinary differential equations to model a system of partial differential equations. As a case study, the fractal fractional Schnakenberg system is formulated with the Caputo operator (in terms of the power law), the Caputo-Fabrizio operator (with exponential decay law) and the Atangana-Baleanu fractional derivative (based on the Mittag-Liffler law). We design some algorithms for the Schnakenberg model by using the newly proposed numerical methods. In such schemes, it worth mentioning that the classical cases are recovered whenever α=1 and β=1. Numerical results obtained for different fractal-order (β∈(0,1)) and fractional-order (α∈(0,1)) are also given to address any point and query that may arise.http://www.sciencedirect.com/science/article/pii/S111001682030121634A3435A0535K5765L0565M0693C10 |
| spellingShingle | Kolade M. Owolabi Abdon Atangana Ali Akgul Modelling and analysis of fractal-fractional partial differential equations: Application to reaction-diffusion model Alexandria Engineering Journal 34A34 35A05 35K57 65L05 65M06 93C10 |
| title | Modelling and analysis of fractal-fractional partial differential equations: Application to reaction-diffusion model |
| title_full | Modelling and analysis of fractal-fractional partial differential equations: Application to reaction-diffusion model |
| title_fullStr | Modelling and analysis of fractal-fractional partial differential equations: Application to reaction-diffusion model |
| title_full_unstemmed | Modelling and analysis of fractal-fractional partial differential equations: Application to reaction-diffusion model |
| title_short | Modelling and analysis of fractal-fractional partial differential equations: Application to reaction-diffusion model |
| title_sort | modelling and analysis of fractal fractional partial differential equations application to reaction diffusion model |
| topic | 34A34 35A05 35K57 65L05 65M06 93C10 |
| url | http://www.sciencedirect.com/science/article/pii/S1110016820301216 |
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