Fractional dynamics in complex media: a meshless numerical framework for distributed-order models with Riesz diffusion.
Saved in:
| Title: | Fractional dynamics in complex media: a meshless numerical framework for distributed-order models with Riesz diffusion. |
|---|---|
| Authors: | Derakhshan, Mohammad Hossein1 (AUTHOR) M.h.derakhshan.20@gmail.com, Irandoust Pakchin, Safar1 (AUTHOR) |
| Source: | Soft Computing - A Fusion of Foundations, Methodologies & Applications. Jun2026, Vol. 30 Issue 6, p3929-3950. 22p. |
| Subjects: | Caputo fractional derivatives, Meshfree methods, Numerical analysis, Fractional calculus, Fick's laws of diffusion, Operator theory, Fractional differential equations |
| Abstract: | This work investigates a three-dimensional coupled system of distributed-order fractional differential equations involving Caputo-type time derivatives and Riesz fractional spatial operators. The model is designed to capture complex physical phenomena characterized by memory effects and spatial nonlocality, which commonly arise in applications such as porous media flow, viscoelastic materials, and anomalous diffusion processes. To efficiently solve this system, we develop a fully discrete numerical scheme that integrates a high-order temporal discretization based on quadrature approximations of the distributed-order Caputo derivatives with a meshless collocation method for spatial discretization. The proposed approach offers flexibility in handling irregular geometries without the need for structured grids. Rigorous convergence and stability analyses are presented, yielding optimal error estimates under suitable regularity assumptions. Numerical experiments are performed to validate the accuracy and efficiency of the method, including tests with both exact solutions and more realistic scenarios lacking analytical solutions. The results demonstrate that the proposed scheme is accurate, stable, and computationally efficient, making it well suited for practical applications involving high-dimensional, nonlocal fractional systems. [ABSTRACT FROM AUTHOR] |
| Copyright of Soft Computing - A Fusion of Foundations, Methodologies & Applications is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
| FullText | Text: Availability: 0 |
|---|---|
| Header | DbId: egs DbLabel: Engineering Source An: 195076866 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
| IllustrationInfo | |
| Items | – Name: Title Label: Title Group: Ti Data: Fractional dynamics in complex media: a meshless numerical framework for distributed-order models with Riesz diffusion. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Derakhshan%2C+Mohammad+Hossein%22">Derakhshan, Mohammad Hossein</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> M.h.derakhshan.20@gmail.com</i><br /><searchLink fieldCode="AR" term="%22Irandoust+Pakchin%2C+Safar%22">Irandoust Pakchin, Safar</searchLink><relatesTo>1</relatesTo> (AUTHOR) – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Soft+Computing+-+A+Fusion+of+Foundations%2C+Methodologies+%26+Applications%22">Soft Computing - A Fusion of Foundations, Methodologies & Applications</searchLink>. Jun2026, Vol. 30 Issue 6, p3929-3950. 22p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Caputo+fractional+derivatives%22">Caputo fractional derivatives</searchLink><br /><searchLink fieldCode="DE" term="%22Meshfree+methods%22">Meshfree methods</searchLink><br /><searchLink fieldCode="DE" term="%22Numerical+analysis%22">Numerical analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Fractional+calculus%22">Fractional calculus</searchLink><br /><searchLink fieldCode="DE" term="%22Fick's+laws+of+diffusion%22">Fick's laws of diffusion</searchLink><br /><searchLink fieldCode="DE" term="%22Operator+theory%22">Operator theory</searchLink><br /><searchLink fieldCode="DE" term="%22Fractional+differential+equations%22">Fractional differential equations</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: This work investigates a three-dimensional coupled system of distributed-order fractional differential equations involving Caputo-type time derivatives and Riesz fractional spatial operators. The model is designed to capture complex physical phenomena characterized by memory effects and spatial nonlocality, which commonly arise in applications such as porous media flow, viscoelastic materials, and anomalous diffusion processes. To efficiently solve this system, we develop a fully discrete numerical scheme that integrates a high-order temporal discretization based on quadrature approximations of the distributed-order Caputo derivatives with a meshless collocation method for spatial discretization. The proposed approach offers flexibility in handling irregular geometries without the need for structured grids. Rigorous convergence and stability analyses are presented, yielding optimal error estimates under suitable regularity assumptions. Numerical experiments are performed to validate the accuracy and efficiency of the method, including tests with both exact solutions and more realistic scenarios lacking analytical solutions. The results demonstrate that the proposed scheme is accurate, stable, and computationally efficient, making it well suited for practical applications involving high-dimensional, nonlocal fractional systems. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Soft Computing - A Fusion of Foundations, Methodologies & Applications is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
| PLink | https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=egs&AN=195076866 |
| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1007/s00500-025-11062-4 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 22 StartPage: 3929 Subjects: – SubjectFull: Caputo fractional derivatives Type: general – SubjectFull: Meshfree methods Type: general – SubjectFull: Numerical analysis Type: general – SubjectFull: Fractional calculus Type: general – SubjectFull: Fick's laws of diffusion Type: general – SubjectFull: Operator theory Type: general – SubjectFull: Fractional differential equations Type: general Titles: – TitleFull: Fractional dynamics in complex media: a meshless numerical framework for distributed-order models with Riesz diffusion. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Derakhshan, Mohammad Hossein – PersonEntity: Name: NameFull: Irandoust Pakchin, Safar IsPartOfRelationships: – BibEntity: Dates: – D: 15 M: 06 Text: Jun2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 14327643 Numbering: – Type: volume Value: 30 – Type: issue Value: 6 Titles: – TitleFull: Soft Computing - A Fusion of Foundations, Methodologies & Applications Type: main |
| ResultId | 1 |
