Year: 2022
Type: article
Abstract: The current manuscript is concerned with the development of the Newton–Raphson method, playing a significant role in mathematics and various other disciplines such as optimization, by using fractional derivatives and fractional Taylor series expansion. The development and modification of the Newton–Raphson method allow us to establish two new methods, which are called first‐ and second‐order fractional Newton–Raphson (FNR) methods. We provide convergence analysis of first‐ and second‐order fractional methods and give a general condition for the convergence of higher‐order FNR. Finally, some illustrative examples are considered to confirm the accuracy and effectiveness of both methods.
Source: Journal of Mathematics
DOI: 10.1155/2022/7070253
Authors: Mine Aylin Bayrak, Ali Demir, Ebru Ozbilge
Institutions: Kocaeli Üniversitesi, American University of the Middle East
Language: English
Subfield: Numerical Analysis
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $2,160
OpenAlex ID: W4309524119