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Review on Recent Advances in Fractional Differentiation and its Applications |
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PP: 245-261 |
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doi:10.18576/pfda/110203
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Author(s) |
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Mohamed Hafez,
Faisal Alshowaikh,
Betty Wan Niu Voon,
Shawkat Alkhazaleh,
Hussein Al-Faiz,
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Abstract |
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| This article comprehensively reviews recent developments in fractional differentiation, focusing on its mathematical basis and applications in many fields. Fractional differentiation extends traditional mathematics to include non-integer order derivatives to provide improved complex systems modeling capabilities. The introduction explains the importance of fractional calculus in both theoretical and practical terms. The article presents fractional differentiation, discusses its characteristics, traces its historical development, and provides background information. The article then examines the basic fractional computation operators, including the Riemann-Liouville and Caputo operators, essential to understanding the statistical process. Moreover, we focus on numerical methods for phase differences, describing finite difference schemes and spectral methods that facilitate computational applications. These methods are developed through examples of physical phenomena, such as wave propagation and effects, and signaling functions and systems used in the industrial sector. They determine how differentiation is applied to the relevant industrial context. In addition, the article examines the impact on the ecosystem wom and medicine, especially biomechanics and biomedical imaging. A good-sized emphasis is placed on the rising position of fractional differentiation in device getting to know, showcasing its ability to enhance algorithmic performance. Finally, the object addresses modern challenges and describes future instructions for research, emphasizing the need for further exploration and innovation in this dynamic area. By synthesizing current findings, this review aims to provide a valuable aid for researchers and practitioners interested in fractional differentiation’s theoretical and sensible implications. |
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