Department of Mathematics and Computer Science, Faculty of Science, Menoufia University, Egypt.
Gofa Camp, Near Gofa Industrial College and German Adebabay, Nifas Silk-Lafto, 26649 Addis Ababa, Ethiopia.
Comput Math Methods Med. 2022 Jul 22;2022:2138775. doi: 10.1155/2022/2138775. eCollection 2022.
Recently, a generalized fractional derivative formulation, known as Abu-Shady-Kaabar fractional derivative, is studied in detail which produces satisfactory results that are consistent with conventional definitions of fractional derivative such as Caputo and Riemann-Liouville. To derive the fractional forms of special functions, the generalized fractional derivative is used. The findings demonstrate that the current findings are compatible with Caputo findings. In addition, the fractional solution to the Bessel equation is found. While modeling phenomena in engineering, physical, and health sciences, special functions can be encountered in most modeling scenarios related to electromagnetic waves, hydrodynamics, and other related models. Therefore, there is a need for a computational tool for computing special functions in the sense of fractional calculus. This tool provides a straightforward technique for some fractional-order special functions while modeling these scientific phenomena in science, medicine, and engineering.
最近，详细研究了一种广义分数导数公式，即 Abu-Shady-Kaabar 分数导数，它产生了与传统分数导数定义（如 Caputo 和 Riemann-Liouville）一致的令人满意的结果。为了推导出特殊函数的分数形式，使用了广义分数导数。研究结果表明，目前的结果与 Caputo 的结果一致。此外，还找到了贝塞尔方程的分数解。在工程、物理和健康科学中的现象建模中，在与电磁波、流体动力学和其他相关模型相关的大多数建模场景中都可能遇到特殊函数。因此，需要有一种计算特殊函数的计算工具，以分数阶微积分的意义。该工具为某些分数阶特殊函数提供了一种简单的技术，用于在科学、医学和工程中对这些科学现象进行建模。
