Titlebook: Intelligent Numerical Methods: Applications to Fractional Calculus; George A. Anastassiou,Ioannis K. Argyros Book 2016 Springer Internatio

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Secant-Like Methods and Modified ,-Fractional Calculus,We present local and semilocal convergence results for secant-type methods in order to approximate a locally unique solution of a nonlinear equation in a Banach space setting.

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Secant-Like Methods and Generalized ,-Fractional Calculus of Canavati-Type,We present local and semilocal convergence results for secant-like methods in order to approximate a locally unique solution of a nonlinear equation in a Banach space setting. Finally, we present some applications from generalized .-fractional calculus involving Canavati-type functions. It follows [.].

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Iterative Algorithms and Left-Right Caputo Fractional Derivatives,We present a local as well as a semilocal convergence analysis for some iterative algorithms in order to approximate a locally unique solution.

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Iterative Methods on Banach Spaces with a Convergence Structure and Fractional Calculus,We present a semilocal convergence for some iterative methods on a Banach space with a convergence structure.

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The Asymptotic Mesh Independence Principle,We present a new asymptotic mesh independence principle of Newton’s method for discretized nonlinear operator equations. Our hypotheses are weaker than in earlier studies such as [., .–.].

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