Mathematical and Physical Analysis of the Fractional Dynamical Model
This paper consists of various kinds of wave solitons to the mathematical model known as the truncated M-fractional FitzHugh–Nagumo model. This model explains the transmission of the electromechanical pulses in nerves. Through the application of the modified extended tanh function technique and the...
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| Format: | Article |
| Language: | English |
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MDPI AG
2025-07-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/9/7/453 |
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| author | Mohammed Ahmed Alomair Haitham Qawaqneh |
| author_facet | Mohammed Ahmed Alomair Haitham Qawaqneh |
| author_sort | Mohammed Ahmed Alomair |
| collection | DOAJ |
| description | This paper consists of various kinds of wave solitons to the mathematical model known as the truncated M-fractional FitzHugh–Nagumo model. This model explains the transmission of the electromechanical pulses in nerves. Through the application of the modified extended tanh function technique and the modified <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><msup><mi>G</mi><mo>′</mo></msup><mo>/</mo><msup><mi>G</mi><mn>2</mn></msup><mo>)</mo></mrow></semantics></math></inline-formula>-expansion technique, we are able to achieve the series of exact solitons. The results differ from the current solutions because of the fractional derivative. These solutions could be helpful in the telecommunication and bioscience domains. Contour plots, in two and three dimensions, are used to describe the results. Stability analysis is used to check the stability of the obtained solutions. Moreover, the stationary solutions of the focusing equation are studied through modulation instability. Future research on the focused model in question will benefit from the findings. The techniques used are simple and effective. |
| format | Article |
| id | doaj-art-afb9b7febadc4248a17a4ca21892ef89 |
| institution | Kabale University |
| issn | 2504-3110 |
| language | English |
| publishDate | 2025-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj-art-afb9b7febadc4248a17a4ca21892ef892025-08-20T03:58:26ZengMDPI AGFractal and Fractional2504-31102025-07-019745310.3390/fractalfract9070453Mathematical and Physical Analysis of the Fractional Dynamical ModelMohammed Ahmed Alomair0Haitham Qawaqneh1Department of Quantitative Methods, School of Business, King Faisal University, Al-Ahsa 31982, Saudi ArabiaDepartment of Mathematics, Faculty of Science and Information Technology, Al-Zaytoonah University of Jordan, Amman 11733, JordanThis paper consists of various kinds of wave solitons to the mathematical model known as the truncated M-fractional FitzHugh–Nagumo model. This model explains the transmission of the electromechanical pulses in nerves. Through the application of the modified extended tanh function technique and the modified <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><msup><mi>G</mi><mo>′</mo></msup><mo>/</mo><msup><mi>G</mi><mn>2</mn></msup><mo>)</mo></mrow></semantics></math></inline-formula>-expansion technique, we are able to achieve the series of exact solitons. The results differ from the current solutions because of the fractional derivative. These solutions could be helpful in the telecommunication and bioscience domains. Contour plots, in two and three dimensions, are used to describe the results. Stability analysis is used to check the stability of the obtained solutions. Moreover, the stationary solutions of the focusing equation are studied through modulation instability. Future research on the focused model in question will benefit from the findings. The techniques used are simple and effective.https://www.mdpi.com/2504-3110/9/7/453fractional FitzHugh–Nagumo modelmathematical methodsqualitative analysisanalytical solutions |
| spellingShingle | Mohammed Ahmed Alomair Haitham Qawaqneh Mathematical and Physical Analysis of the Fractional Dynamical Model Fractal and Fractional fractional FitzHugh–Nagumo model mathematical methods qualitative analysis analytical solutions |
| title | Mathematical and Physical Analysis of the Fractional Dynamical Model |
| title_full | Mathematical and Physical Analysis of the Fractional Dynamical Model |
| title_fullStr | Mathematical and Physical Analysis of the Fractional Dynamical Model |
| title_full_unstemmed | Mathematical and Physical Analysis of the Fractional Dynamical Model |
| title_short | Mathematical and Physical Analysis of the Fractional Dynamical Model |
| title_sort | mathematical and physical analysis of the fractional dynamical model |
| topic | fractional FitzHugh–Nagumo model mathematical methods qualitative analysis analytical solutions |
| url | https://www.mdpi.com/2504-3110/9/7/453 |
| work_keys_str_mv | AT mohammedahmedalomair mathematicalandphysicalanalysisofthefractionaldynamicalmodel AT haithamqawaqneh mathematicalandphysicalanalysisofthefractionaldynamicalmodel |