The Analytical Solutions to the Fractional Kraenkel–Manna–Merle System in Ferromagnetic Materials
In this article, we examine the Kraenkel–Manna–Merle system (KMMS) with an M-truncated derivative (MTD). Our goal is to obtain rational, hyperbolic, and trigonometric solutions by using the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-07-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/7/7/523 |
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| author | Mohammad Alshammari Amjad E. Hamza Clemente Cesarano Elkhateeb S. Aly Wael W. Mohammed |
| author_facet | Mohammad Alshammari Amjad E. Hamza Clemente Cesarano Elkhateeb S. Aly Wael W. Mohammed |
| author_sort | Mohammad Alshammari |
| collection | DOAJ |
| description | In this article, we examine the Kraenkel–Manna–Merle system (KMMS) with an M-truncated derivative (MTD). Our goal is to obtain rational, hyperbolic, and trigonometric solutions by using the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">F</mi></semantics></math></inline-formula>-expansion technique with the Riccati equation. To our knowledge, no one has studied the exact solutions to the KMMS in the presence/absence of a damping effect with an M-truncated derivative, using the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">F</mi></semantics></math></inline-formula>-expansion technique. The magnetic field propagation in a zero-conductivity ferromagnet is described by the KMMS; hence, solutions to this equation may provide light on several fascinating scientific phenomena. We use MATLAB to display figures in a variety of 3D and 2D formats to demonstrate the influence of the M-truncated derivative on the exact solutions to the KMMS. |
| first_indexed | 2024-03-11T01:03:20Z |
| format | Article |
| id | doaj.art-0df7e3779ad54bf4ae2854e8e137c07c |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-11T01:03:20Z |
| publishDate | 2023-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-0df7e3779ad54bf4ae2854e8e137c07c2023-11-18T19:25:56ZengMDPI AGFractal and Fractional2504-31102023-07-017752310.3390/fractalfract7070523The Analytical Solutions to the Fractional Kraenkel–Manna–Merle System in Ferromagnetic MaterialsMohammad Alshammari0Amjad E. Hamza1Clemente Cesarano2Elkhateeb S. Aly3Wael W. Mohammed4Department of Mathematics, Collage of Science, University of Ha’il, Ha’il 2440, Saudi ArabiaDepartment of Mathematics, Collage of Science, University of Ha’il, Ha’il 2440, Saudi ArabiaSection of Mathematics, International Telematic University Uninettuno, Corso Vittorio Emanuele II, 39, 00186 Roma, ItalyDepartment of Mathematics, Collage of Science, Jazan University, Jazan 45142, Saudi ArabiaDepartment of Mathematics, Collage of Science, University of Ha’il, Ha’il 2440, Saudi ArabiaIn this article, we examine the Kraenkel–Manna–Merle system (KMMS) with an M-truncated derivative (MTD). Our goal is to obtain rational, hyperbolic, and trigonometric solutions by using the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">F</mi></semantics></math></inline-formula>-expansion technique with the Riccati equation. To our knowledge, no one has studied the exact solutions to the KMMS in the presence/absence of a damping effect with an M-truncated derivative, using the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">F</mi></semantics></math></inline-formula>-expansion technique. The magnetic field propagation in a zero-conductivity ferromagnet is described by the KMMS; hence, solutions to this equation may provide light on several fascinating scientific phenomena. We use MATLAB to display figures in a variety of 3D and 2D formats to demonstrate the influence of the M-truncated derivative on the exact solutions to the KMMS.https://www.mdpi.com/2504-3110/7/7/523fractional KMMSℱ-expansion methodM-truncated derivative |
| spellingShingle | Mohammad Alshammari Amjad E. Hamza Clemente Cesarano Elkhateeb S. Aly Wael W. Mohammed The Analytical Solutions to the Fractional Kraenkel–Manna–Merle System in Ferromagnetic Materials Fractal and Fractional fractional KMMS ℱ-expansion method M-truncated derivative |
| title | The Analytical Solutions to the Fractional Kraenkel–Manna–Merle System in Ferromagnetic Materials |
| title_full | The Analytical Solutions to the Fractional Kraenkel–Manna–Merle System in Ferromagnetic Materials |
| title_fullStr | The Analytical Solutions to the Fractional Kraenkel–Manna–Merle System in Ferromagnetic Materials |
| title_full_unstemmed | The Analytical Solutions to the Fractional Kraenkel–Manna–Merle System in Ferromagnetic Materials |
| title_short | The Analytical Solutions to the Fractional Kraenkel–Manna–Merle System in Ferromagnetic Materials |
| title_sort | analytical solutions to the fractional kraenkel manna merle system in ferromagnetic materials |
| topic | fractional KMMS ℱ-expansion method M-truncated derivative |
| url | https://www.mdpi.com/2504-3110/7/7/523 |
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