Work

A Modified Fractional Newton’s Solver

Year: 2024

Type: article

Abstract: Fractional calculus extends the conventional concepts of derivatives and integrals to non-integer orders, providing a robust mathematical framework for modeling complex systems characterized by memory and hereditary properties. This study enhances the convergence rate of the Caputo-based Newton’s solver for solving one-dimensional nonlinear equations. By modifying the order to 1+η, we provide a thorough analysis of the convergence order and present numerical simulations that demonstrate the improved efficiency of the proposed modified fractional Newton’s solver. The numerical simulations indicate significant advancements over traditional and existing fractional Newton-type approaches.

Source: Axioms

DOI: 10.3390/axioms13100689

Authors: Chih-Wen Chang, Sania Qureshi, Ioannis K. Argyros, Khair Muhammad Saraz, Evren Hincal

Institutions: National United University, Lebanese American University, Near East University, Cameron University, Mehran University of Engineering and Technology

Language: English

Topic: Iterative Methods for Nonlinear Equations

Subfield: Numerical Analysis

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,728

Funder: National Science and Technology Council