Analytical Techniques for Studying Fractional-Order Jaulent–Miodek System Within Algebraic Context
The proposed study seeks to investigate various analytical and numerical techniques for solving fractional differential equations, with a particular focus on their applications in mathematical modeling and scientific research within the field of algebra. This study intends to investigate methods suc...
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| Format: | Article |
| Language: | English |
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MDPI AG
2025-01-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/9/1/50 |
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| author | Yousuf Alkhezi Ahmad Shafee |
| author_facet | Yousuf Alkhezi Ahmad Shafee |
| author_sort | Yousuf Alkhezi |
| collection | DOAJ |
| description | The proposed study seeks to investigate various analytical and numerical techniques for solving fractional differential equations, with a particular focus on their applications in mathematical modeling and scientific research within the field of algebra. This study intends to investigate methods such as the Aboodh transform iteration method and the Aboodh residual power series method, specifically for addressing the Jaulent–Miodek system of partial differential equations. By analyzing the behavior of fractional-order differential equations and their solutions, this research seeks to contribute to a deeper understanding of complex mathematical phenomena. Furthermore, this study examines the role of the Caputo operator in fractional calculus, offering insights into its significance in modeling real-world systems within the algebraic context. Through this research, novel approaches for solving fractional differential equations are developed, offering essential tools for researchers in diverse fields of science and engineering, including algebraic applications. |
| format | Article |
| id | doaj-art-86f51f721b0e46dabf909e976295eba2 |
| institution | Kabale University |
| issn | 2504-3110 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj-art-86f51f721b0e46dabf909e976295eba22025-01-24T13:33:30ZengMDPI AGFractal and Fractional2504-31102025-01-01915010.3390/fractalfract9010050Analytical Techniques for Studying Fractional-Order Jaulent–Miodek System Within Algebraic ContextYousuf Alkhezi0Ahmad Shafee1Mathematics Department, College of Basic Education, Public Authority for Applied Education and Training (PAAET), Ardiya 70654, KuwaitLaboratory Technology Department, College of Technological Studies, Public Authority for Applied Education and Training (PAAET), Shuwaikh 70654, KuwaitThe proposed study seeks to investigate various analytical and numerical techniques for solving fractional differential equations, with a particular focus on their applications in mathematical modeling and scientific research within the field of algebra. This study intends to investigate methods such as the Aboodh transform iteration method and the Aboodh residual power series method, specifically for addressing the Jaulent–Miodek system of partial differential equations. By analyzing the behavior of fractional-order differential equations and their solutions, this research seeks to contribute to a deeper understanding of complex mathematical phenomena. Furthermore, this study examines the role of the Caputo operator in fractional calculus, offering insights into its significance in modeling real-world systems within the algebraic context. Through this research, novel approaches for solving fractional differential equations are developed, offering essential tools for researchers in diverse fields of science and engineering, including algebraic applications.https://www.mdpi.com/2504-3110/9/1/50Jaulent–Miodek system of partial differential equationsiteration transform methodresidual power series transform methodfractional Caputo operatoralgebraic applications |
| spellingShingle | Yousuf Alkhezi Ahmad Shafee Analytical Techniques for Studying Fractional-Order Jaulent–Miodek System Within Algebraic Context Fractal and Fractional Jaulent–Miodek system of partial differential equations iteration transform method residual power series transform method fractional Caputo operator algebraic applications |
| title | Analytical Techniques for Studying Fractional-Order Jaulent–Miodek System Within Algebraic Context |
| title_full | Analytical Techniques for Studying Fractional-Order Jaulent–Miodek System Within Algebraic Context |
| title_fullStr | Analytical Techniques for Studying Fractional-Order Jaulent–Miodek System Within Algebraic Context |
| title_full_unstemmed | Analytical Techniques for Studying Fractional-Order Jaulent–Miodek System Within Algebraic Context |
| title_short | Analytical Techniques for Studying Fractional-Order Jaulent–Miodek System Within Algebraic Context |
| title_sort | analytical techniques for studying fractional order jaulent miodek system within algebraic context |
| topic | Jaulent–Miodek system of partial differential equations iteration transform method residual power series transform method fractional Caputo operator algebraic applications |
| url | https://www.mdpi.com/2504-3110/9/1/50 |
| work_keys_str_mv | AT yousufalkhezi analyticaltechniquesforstudyingfractionalorderjaulentmiodeksystemwithinalgebraiccontext AT ahmadshafee analyticaltechniquesforstudyingfractionalorderjaulentmiodeksystemwithinalgebraiccontext |