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Mathematical analysis of the reaction–diffusion Brusselator system within conformable operator.

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Title: Mathematical analysis of the reaction–diffusion Brusselator system within conformable operator.
Authors: Almusawa, Musawa Yahya1 (AUTHOR), Alqudah, Mohammad2 (AUTHOR), Almusawa, Hassan1 (AUTHOR), Shafee, Ahmad3 (AUTHOR) as.zada@paaet.edu.kw, Almarashi, Adel1 (AUTHOR)
Source: Pramana: Journal of Physics. Jun2026, Vol. 100 Issue 2, p1-25. 25p.
Subjects: Reaction-diffusion equations, Partial differential equations, Iterative methods (Mathematics), Computational mathematics, Biomathematics, Numerical analysis
Abstract: In this paper, we investigate the use of conformable approaches to numerically solve complex systems, namely the two-dimensional reaction–diffusion Brusselator model. In such models, the paper presents a new conformable residual series approach to deal with difficulties in solving nonlinear partial differential equations (PDEs). Also, we present a conformable iterative method, which is aimed to increase the computational efficiency and accuracy of the iterative solver. Using the characteristics of the conformable operator, we can develop a more stable method to truncate the dynamics of reaction–diffusion systems. The paper establishes, through theoretical evaluation and numerical experimentation, the efficacy of the conformable methods in enhancing rates of convergence and stability compare to the traditional techniques. The results in this paper will be useful in the future in both computational mathematics and theoretical biology, especially regarding modelling of biochemical reaction process and ecological dynamics. [ABSTRACT FROM AUTHOR]
Copyright of Pramana: Journal of Physics 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.)
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  Data: Mathematical analysis of the reaction–diffusion Brusselator system within conformable operator.
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  Data: <searchLink fieldCode="JN" term="%22Pramana%3A+Journal+of+Physics%22">Pramana: Journal of Physics</searchLink>. Jun2026, Vol. 100 Issue 2, p1-25. 25p.
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  Data: <searchLink fieldCode="DE" term="%22Reaction-diffusion+equations%22">Reaction-diffusion equations</searchLink><br /><searchLink fieldCode="DE" term="%22Partial+differential+equations%22">Partial differential equations</searchLink><br /><searchLink fieldCode="DE" term="%22Iterative+methods+%28Mathematics%29%22">Iterative methods (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Computational+mathematics%22">Computational mathematics</searchLink><br /><searchLink fieldCode="DE" term="%22Biomathematics%22">Biomathematics</searchLink><br /><searchLink fieldCode="DE" term="%22Numerical+analysis%22">Numerical analysis</searchLink>
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  Data: In this paper, we investigate the use of conformable approaches to numerically solve complex systems, namely the two-dimensional reaction–diffusion Brusselator model. In such models, the paper presents a new conformable residual series approach to deal with difficulties in solving nonlinear partial differential equations (PDEs). Also, we present a conformable iterative method, which is aimed to increase the computational efficiency and accuracy of the iterative solver. Using the characteristics of the conformable operator, we can develop a more stable method to truncate the dynamics of reaction–diffusion systems. The paper establishes, through theoretical evaluation and numerical experimentation, the efficacy of the conformable methods in enhancing rates of convergence and stability compare to the traditional techniques. The results in this paper will be useful in the future in both computational mathematics and theoretical biology, especially regarding modelling of biochemical reaction process and ecological dynamics. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Pramana: Journal of Physics 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.)
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        Value: 10.1007/s12043-025-03041-z
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      – Code: eng
        Text: English
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      – SubjectFull: Reaction-diffusion equations
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      – SubjectFull: Partial differential equations
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      – SubjectFull: Iterative methods (Mathematics)
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      – SubjectFull: Computational mathematics
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      – SubjectFull: Numerical analysis
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      – TitleFull: Mathematical analysis of the reaction–diffusion Brusselator system within conformable operator.
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            NameFull: Almusawa, Musawa Yahya
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              M: 06
              Text: Jun2026
              Type: published
              Y: 2026
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