Generalized \(g\)-fractional calculus of Canavati-type and secant-like methods

DOI10.1007/S40819-016-0214-3zbMath1397.65078OpenAlexW2476627790MaRDI QIDQ1791774

George A. Anastassiou, Ioannis K. Argyros

Publication date: 11 October 2018

Published in: International Journal of Applied and Computational Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s40819-016-0214-3

zbMATH Keywords

Banach spacefractional calculusgeneralized fractional derivativessecant-like methodsemilocal-local convergence

Mathematics Subject Classification ID

Numerical computation of solutions to systems of equations (65H10) Iterative procedures involving nonlinear operators (47J25) Equations involving nonlinear operators (general) (47J05) Fractional derivatives and integrals (26A33) Numerical solutions to equations with nonlinear operators (65J15)

Cites Work

• Different anomalies in a Jarratt family of iterative root-finding methods
• A new tool to study real dynamics: the convergence plane
• Fractional representation formulae and right fractional inequalities
• The analysis of fractional differential equations. An application-oriented exposition using differential operators of Caputo type
• Chaotic dynamics of a third-order Newton-type method
• Newton-type methods of high order and domains of semilocal and global convergence
• Third-order iterative methods under Kantorovich conditions
• New general convergence theory for iterative processes and its applications to Newton-Kantorovich type theorems
• Convergence and Applications of Newton-type Iterations
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