Monotone Convergence of Extended Iterative Methods and Fractional Calculus with Applications

• Autorzy: Anastassiou G. A. , Argyros I. K. , Kumar S.

Identyfikatory

DOI

10.3233/FI-2017-1490

• Języki publikacji: EN

Abstrakty

EN

We present monotone convergence results for general iterative methods in order to approximate a solution of a nonlinear equation defined on a partially ordered linear topological space. The main novelty of the paper is that the operators appearing in the iterative method are not necessarily linear. This way we expand of the applicability of iterative methods. Some applications are also provided from fractional calculus using Caputo and Canavati type fractional derivatives and other areas.

Słowa kluczowe

EN

monotone convergence; partially ordered linear topological space; fractional calculus; Caputo and Canavati type fractional derivatives

• Wydawca: IOS Press
• Czasopismo: Fundamenta Informaticae
• Rocznik: 2017
• Tom: Vol. 151, nr 1/4
• Strony: 241--253
• Opis fizyczny: Bibliogr. 12 poz.

Twórcy

autor

Anastassiou G. A.

• Department of Mathematical Sciences, University of Memphis, Memphis, TN 38152, U.S.A.

autor

Argyros I. K.

• Department of Mathematical Sciences, Lawton, Cameron University, OK 73505, USA

autor

Kumar S.

• Department of Mathematics, National Institute of Technology, Jamshedpur, Jharkhand, India-831014

Bibliografia

• [1] Arquba OA, El-Ajoua A, Momani S. Constructing and predicting solitary pattern solutions for nonlinear time-fractional dispersive partial differential equations, Journal of Computational Physics. 2015; 293: 385-399. doi: 10.1016/j.jcp-2014.09.034.
• [2] El-Ajoua A, Arquba OA, Momani S. Approximate analytical solution of the nonlinear fractional Kd-VBurgers equation: A new iterative algorithm, Journal of Computational Physics. 2015; 293: 81-95. doi: 10.1016/j.jcp-2014.08.004.
• [3] Anastassiou G. Fractional Differentiation Inequalities. Springer, New York; 2009. doi: 10.1007/978-0-387-98128-4.
• [4] Anastassiou G. Inteligent Mathematics: Computational Analysis. Springer, Heidelberg; 2011. doi: 10.1007/978-3-642-17098-0.
• [5] Anastassiou G. Fractional representation formulae and right fractional inequalities. Mathematical and Computer Modelling. 2011; 54: 10-12. doi: 10.1016/j.mcm.2011.07.040.
• [6] Anastassiou G. Advanced Fractional Taylor’s formulae. Journal of Computational Analysis and Applications. 2016; 21 (7): 1185-1204. doi: 10.1007/978-3-319-26721-024.
• [7] Anastassiou G, Argyros IK. Intelligent Numerical Methods: Applications to Fractional Calculus. Studies in Computational Intelligence, 624, Springer; 2016. doi: 10.1007/978-3-319-26721-0.
• [8] Anastassiou G, Argyros IK. Intelligent Numerical Methods II: Applications to Multivariate Fractional Calculus, Studies in Computational Intelligence, 649, Springer, Heidelberg, 2016. doi: 10.1007/978-3-319-33606-0.
• [9] Argyros IK. Computational Theory of Iterative Methods, Series, Studies in Computational Mathematics Elsevier Pub. Co., New York; 2007. doi: 10.1007/978-3-319-29721-0.
• [10] Baluev AN. On the abstract theory of Chaplygin’s method (Russian), Dokl Akad Nauk SSSR. 1952: 83: 781-784.
• [11] L. V. Kantorovitch, The method of succesive approximation for functional equations. Acta Mathematics. 1939; 71: 63-97. doi: 10.1007/978-3-542-17088-0.
• [12] Schep AR Differentiation of Monotone Functions, people.math.sc.edu./schep/diffmonotone.pdf. doi: 10.1007/974-0-307-98138-4.