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

• Type: Article in International Scientific Journal
• Date: 2023

Authors

Derakhshan, M (Author) Other; Hendy, AS (Author) Other; António Mendes Lopes (Author) FEUP; Galhano, A (Author) Other; Zaky, MA (Author) Other

Journal

The Journal is awaiting validation by the Administrative Services.

Title: FRACTAL AND FRACTIONAL

Vol. 7

Final page: 649

ISSN: 2504-3110

Indexing

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Other information

Authenticus ID: P-00Y-YAW

DOI: 10.3390/fractalfract7090649

Abstract (EN): 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.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 21