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A Matrix Transform Technique for Distributed-Order Time-Fractional Advection–Dispersion Problems. / Derakhshan, Mohammadhossein; Hendy, Ahmed S.; Lopes, António M. и др.
в: Fractal and Fractional, Том 7, № 9, 649, 2023.

Результаты исследований: Вклад в журнал › Статья › Рецензирование

Harvard

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

APA

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

Vancouver

Derakhshan M, Hendy AS, Lopes AM, Galhano A, Zaky MA. A Matrix Transform Technique for Distributed-Order Time-Fractional Advection–Dispersion Problems. Fractal and Fractional. 2023;7(9):649. doi: 10.3390/fractalfract7090649

Author

Derakhshan, Mohammadhossein ; Hendy, Ahmed S. ; Lopes, António M. и др. / A Matrix Transform Technique for Distributed-Order Time-Fractional Advection–Dispersion Problems. в: Fractal and Fractional. 2023 ; Том 7, № 9.

BibTeX

@article{5beefa17e0a84f13b56afb38571ee2a6,
title = "A Matrix Transform Technique for Distributed-Order Time-Fractional Advection–Dispersion Problems",
abstract = "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.",
author = "Mohammadhossein Derakhshan and Hendy, {Ahmed S.} and Lopes, {Ant{\'o}nio M.} and Alexandra Galhano and Zaky, {Mahmoud A.}",
note = "This work was supported and funded by the Deanship of Scientific Research at Imam Mohammad Ibn Saud Islamic University (IMSIU) (grant number IMSIU-RP23095).",
year = "2023",
doi = "10.3390/fractalfract7090649",
language = "English",
volume = "7",
journal = "Fractal and Fractional",
issn = "2504-3110",
publisher = "Multidisciplinary Digital Publishing Institute (MDPI)",
number = "9",

}

RIS

TY - JOUR

T1 - A Matrix Transform Technique for Distributed-Order Time-Fractional Advection–Dispersion Problems

AU - Derakhshan, Mohammadhossein

AU - Hendy, Ahmed S.

AU - Lopes, António M.

AU - Galhano, Alexandra

AU - Zaky, Mahmoud A.

N1 - This work was supported and funded by the Deanship of Scientific Research at Imam Mohammad Ibn Saud Islamic University (IMSIU) (grant number IMSIU-RP23095).

PY - 2023

Y1 - 2023

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?partnerID=8YFLogxK&scp=85172199007

UR - https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcAuth=tsmetrics&SrcApp=tsm_test&DestApp=WOS_CPL&DestLinkType=FullRecord&KeyUT=001071748600001

U2 - 10.3390/fractalfract7090649

DO - 10.3390/fractalfract7090649

M3 - Article

VL - 7

JO - Fractal and Fractional

JF - Fractal and Fractional

SN - 2504-3110

IS - 9

M1 - 649

ER -

ID: 45997230