A Matrix Transform Technique for Distributed-Order Time-Fractional Advection–Dispersion Problems
Электронный научный архив УРФУ
Информация об архиве | Просмотр оригинала| Поле | Значение | |
| Заглавие |
A Matrix Transform Technique for Distributed-Order Time-Fractional Advection–Dispersion Problems
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| Автор |
Derakhshan, M.
Hendy, A. S. Lopes, A. M. Galhano, A. Zaky, M. A. |
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| Тематика |
ADVECTION–DISPERSION EQUATION
CONVERGENCE ANALYSIS DISTRIBUTED-ORDER MATRIX TRANSFORM METHOD RIESZ FRACTIONAL DERIVATIVE |
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| Описание |
Invoking the matrix transfer technique, we propose a novel numerical scheme to solve the time-fractional advection–dispersion equation (ADE) with distributed-order Riesz-space fractional derivatives (FDs). The method adopts the midpoint rule to reformulate the distributed-order Riesz-space FDs by means of a second-order linear combination of Riesz-space FDs. Then, a central difference approximation is used side by side with the matrix transform technique for approximating the Riesz-space FDs. Based on this, the distributed-order time-fractional ADE is transformed into a time-fractional ordinary differential equation in the Caputo sense, which has an equivalent Volterra integral form. The Simpson method is used to discretize the weakly singular kernel of the resulting Volterra integral equation. Stability, convergence, and error analysis are presented. Finally, simulations are performed to substantiate the theoretical findings. © 2023 by the authors.
Al-Imam Muhammad Ibn Saud Islamic University, IMSIU; Deanship of Scientific Research, Imam Mohammed Ibn Saud Islamic University: IMSIU-RP23095 The authors gratefully acknowledge the technical and financial support provided by the Deanship of Scientific Research at Imam Mohammad Ibn Saud Islamic University (IMSIU). This work was supported and funded by the Deanship of Scientific Research at Imam Mohammad Ibn Saud Islamic University (IMSIU) (grant number IMSIU-RP23095). |
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| Дата |
2024-04-05T16:32:59Z
2024-04-05T16:32:59Z 2023 |
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| Тип |
Article
Journal article (info:eu-repo/semantics/article) |info:eu-repo/semantics/publishedVersion |
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| Идентификатор |
Derakhshan, M, Hendy, AS, Lopes, AM, Galhano, A & Zaky, MA 2023, 'A Matrix Transform Technique for Distributed-Order Time-Fractional Advection–Dispersion Problems', Fractal and Fractional, Том. 7, № 9, 649. https://doi.org/10.3390/fractalfract7090649
Derakhshan, M., Hendy, A. S., Lopes, A. M., Galhano, A., & Zaky, M. A. (2023). A Matrix Transform Technique for Distributed-Order Time-Fractional Advection–Dispersion Problems. Fractal and Fractional, 7(9), [649]. https://doi.org/10.3390/fractalfract7090649 2504-3110 Final All Open Access, Gold https://www.scopus.com/inward/record.uri?eid=2-s2.0-85172199007&doi=10.3390%2ffractalfract7090649&partnerID=40&md5=338b1e7e2061b07a31bc2da5b3d90e06 https://www.mdpi.com/2504-3110/7/9/649/pdf?version=1692966813 http://elar.urfu.ru/handle/10995/130798 10.3390/fractalfract7090649 85172199007 001071748600001 |
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| Язык |
en
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| Права |
Open access (info:eu-repo/semantics/openAccess)
cc-by https://creativecommons.org/licenses/by/4.0/ |
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| Формат |
application/pdf
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| Издатель |
Multidisciplinary Digital Publishing Institute (MDPI)
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| Источник |
Fractal and Fractional
Fractal and Fractional |
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