On Fractional Newton-Type Method for Nonlinear Problems. (21st November 2022)

• Record Type: Journal Article
• Authors: Bayrak, Mine Aylin; Demir, Ali; Ozbilge, Ebru
• Other Names: Araci Serkan Academic Editor.
• Is Part Of: Journal of mathematics. Volume 2022(2022)
• Publication Date: 2022-11-21
• Subjects: Mathematics -- Periodicals; Mathematics; Periodicals; 510
• DOI: 10.1155/2022/7070253
• Languages: English
• ISSNs: 2314-4629

Abstract

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.