A Short Note on the Quasilinearization Method for Fractional Differential Equations. (1st September 2016)

• Record Type: Journal Article
• Authors: Vijesh, V. Antony
• Is Part Of: Numerical functional analysis and optimization. Volume 37:Number 9(2016)
• Page Start: 1158
• Page End: 1167
• Publication Date: 2016-09-01
• Subjects: Caputo's fractional derivative -- fractional order Riccati equation -- Newton's method -- quasilinearization; 34A08 -- 34A12 -- 65J15; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2016.1188827
• Languages: English
• ISSNs: 0163-0563

Abstract

ABSTRACT: Recent literature shows that for certain classes of fractional differential equations the monotone iterative technique fails to guarantee the quadratic convergence of the quasilinearization method. The present work proves the quadratic convergence of the quasilinearization method and the existence and uniqueness of the solution of such a class of fractional differential equations. Our analysis depends upon the classical Kantorovich theorem on Newton's method. Various examples are discussed in order to illustrate our approach.