An optimal and low computational cost fractional Newton-type method for solving nonlinear equations

DOI10.1016/J.AML.2021.107650zbMath1487.65053OpenAlexW3201151450MaRDI QIDQ2060913

Giro Candelario, Juan Ramón Torregrosa Sánchez, Maria P. Vassileva, Alicia Cordero

Publication date: 13 December 2021

Published in: Applied Mathematics Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aml.2021.107650

zbMATH Keywords

Newton's methodquadratic convergencenonlinear equationsconformable fractional derivative

Mathematics Subject Classification ID

Fractional derivatives and integrals (26A33) Numerical computation of solutions to single equations (65H05)

Related Items (5)

Acceleration of the order of convergence of a family of fractional fixed-point methods and its implementation in the solution of a nonlinear algebraic system related to hybrid solar receivers ⋮ The dynamical analysis of a low computational cost family of higher-order fractional iterative method ⋮ An efficient family of two-step with-memory methods with convergence order 6 and their dynamics ⋮ Generalized conformable fractional Newton-type method for solving nonlinear systems ⋮ A fractional Traub-Steffensen-type method for solving nonlinear equations

Cites Work

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• A new tool to study real dynamics: the convergence plane
• On conformable fractional calculus
• A new definition of fractional derivative
• A fractional Newton method with \(2 \alpha\) th-order of convergence and its stability
• Variants of Newton's method using fifth-order quadrature formulas
• Optimal Order of One-Point and Multipoint Iteration
• A Precision Approximation of the Gamma Function

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