A novel computational tool for the fractional-order special functions arising from modeling scientific phenomena via Abu-Shady-Kaabar fractional derivative
Document Type
Article
Publication Date
7-1-2022
Abstract
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.
Keywords
Definition, Calculus
Publication Title
Computational and Mathematical Methods in Medicine
Volume
2022
Publisher
Hindawi Ltd
Publisher Location
ADAM HOUSE, 3RD FLR, 1 FITZROY SQ, LONDON, W1T 5HF, ENGLAND