A Short Note on the Quasilinearization Method for Fractional Differential Equations

被引：7
|
作者：
Vijesh, V. Antony [1 ]
机构：
[1] Indian Inst Technol Indore, Sch Basic Sci, Indore 452020, Madhya Pradesh, India
来源：
NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION | 2016年 / 37卷 / 09期
关键词：
Caputo's fractional derivative; fractional order Riccati equation; Newton's method; quasilinearization;
D O I：
10.1080/01630563.2016.1188827
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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.
引用
收藏
页码：1158 / 1167
页数：10
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