A Comparative Analysis of Laplace Residual Power Series and a New Iteration Method for Fitzhugh-Nagumo Equation in the Caputo Operator Framework
In this paper, I utilize the Laplace residual power series method (LRPSM) along with a novel iteration technique to investigate the Fitzhugh-Nagumo equation within the framework of the Caputo operator. The Fitzhugh-Nagumo equation is a fundamental model for describing excitable systems, playing a cr...
| প্রধান লেখক: | |
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| বিন্যাস: | প্রবন্ধ |
| ভাষা: | English |
| প্রকাশিত: |
MDPI AG
2023-12-01
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| মালা: | Fractal and Fractional |
| বিষয়গুলি: | |
| অনলাইন ব্যবহার করুন: | https://www.mdpi.com/2504-3110/7/12/867 |
| _version_ | 1827574761727721472 |
|---|---|
| author | Azzh Saad Alshehry |
| author_facet | Azzh Saad Alshehry |
| author_sort | Azzh Saad Alshehry |
| collection | DOAJ |
| description | In this paper, I utilize the Laplace residual power series method (LRPSM) along with a novel iteration technique to investigate the Fitzhugh-Nagumo equation within the framework of the Caputo operator. The Fitzhugh-Nagumo equation is a fundamental model for describing excitable systems, playing a crucial role in understanding various physiological and biological phenomena. The Caputo operator extends the conventional derivative to handle non-local and non-integer-order differential equations, making it a potent tool for modeling complex processes. Our study involves transforming the Fitzhugh-Nagumo equation into its Laplace domain representation, applying the LRPSM to derive a series solution. We then introduce a novel iteration technique to enhance the solution’s convergence properties, enabling more accurate and efficient computations. This approach offers a systematic methodology for solving the Fitzhugh-Nagumo equation with the Caputo operator, providing deeper insights into excitable system dynamics. Numerical examples and comparisons with existing methods demonstrate the accuracy and efficiency of the LRPSM with the new iteration technique, showcasing its potential for solving diverse differential equations involving the Caputo operator and advancing mathematical modeling in various scientific and engineering domains. |
| first_indexed | 2024-03-08T20:45:38Z |
| format | Article |
| id | doaj.art-599c751d28954277983306f4dfd3b5e6 |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-08T20:45:38Z |
| publishDate | 2023-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-599c751d28954277983306f4dfd3b5e62023-12-22T14:10:01ZengMDPI AGFractal and Fractional2504-31102023-12-0171286710.3390/fractalfract7120867A Comparative Analysis of Laplace Residual Power Series and a New Iteration Method for Fitzhugh-Nagumo Equation in the Caputo Operator FrameworkAzzh Saad Alshehry0Department of Mathematical Sciences, Faculty of Sciences, Princess Nourah Bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi ArabiaIn this paper, I utilize the Laplace residual power series method (LRPSM) along with a novel iteration technique to investigate the Fitzhugh-Nagumo equation within the framework of the Caputo operator. The Fitzhugh-Nagumo equation is a fundamental model for describing excitable systems, playing a crucial role in understanding various physiological and biological phenomena. The Caputo operator extends the conventional derivative to handle non-local and non-integer-order differential equations, making it a potent tool for modeling complex processes. Our study involves transforming the Fitzhugh-Nagumo equation into its Laplace domain representation, applying the LRPSM to derive a series solution. We then introduce a novel iteration technique to enhance the solution’s convergence properties, enabling more accurate and efficient computations. This approach offers a systematic methodology for solving the Fitzhugh-Nagumo equation with the Caputo operator, providing deeper insights into excitable system dynamics. Numerical examples and comparisons with existing methods demonstrate the accuracy and efficiency of the LRPSM with the new iteration technique, showcasing its potential for solving diverse differential equations involving the Caputo operator and advancing mathematical modeling in various scientific and engineering domains.https://www.mdpi.com/2504-3110/7/12/867Fitzhugh-Nagumo equationLaplace residual power series methodnew iteration methodCaputo operatorfractional-order differential equation |
| spellingShingle | Azzh Saad Alshehry A Comparative Analysis of Laplace Residual Power Series and a New Iteration Method for Fitzhugh-Nagumo Equation in the Caputo Operator Framework Fractal and Fractional Fitzhugh-Nagumo equation Laplace residual power series method new iteration method Caputo operator fractional-order differential equation |
| title | A Comparative Analysis of Laplace Residual Power Series and a New Iteration Method for Fitzhugh-Nagumo Equation in the Caputo Operator Framework |
| title_full | A Comparative Analysis of Laplace Residual Power Series and a New Iteration Method for Fitzhugh-Nagumo Equation in the Caputo Operator Framework |
| title_fullStr | A Comparative Analysis of Laplace Residual Power Series and a New Iteration Method for Fitzhugh-Nagumo Equation in the Caputo Operator Framework |
| title_full_unstemmed | A Comparative Analysis of Laplace Residual Power Series and a New Iteration Method for Fitzhugh-Nagumo Equation in the Caputo Operator Framework |
| title_short | A Comparative Analysis of Laplace Residual Power Series and a New Iteration Method for Fitzhugh-Nagumo Equation in the Caputo Operator Framework |
| title_sort | comparative analysis of laplace residual power series and a new iteration method for fitzhugh nagumo equation in the caputo operator framework |
| topic | Fitzhugh-Nagumo equation Laplace residual power series method new iteration method Caputo operator fractional-order differential equation |
| url | https://www.mdpi.com/2504-3110/7/12/867 |
| work_keys_str_mv | AT azzhsaadalshehry acomparativeanalysisoflaplaceresidualpowerseriesandanewiterationmethodforfitzhughnagumoequationinthecaputooperatorframework AT azzhsaadalshehry comparativeanalysisoflaplaceresidualpowerseriesandanewiterationmethodforfitzhughnagumoequationinthecaputooperatorframework |