On Fractional Newton-Type Method for Nonlinear Problems

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Bayrak M. A., Demir A., Ozbilge E.

Journal of Mathematics, vol.2022, 2022 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 2022
  • Publication Date: 2022
  • Doi Number: 10.1155/2022/7070253
  • Journal Name: Journal of Mathematics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Kocaeli University Affiliated: Yes


.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.