文章基本信息

标题：Picard iterative processes for initial value problems of singular fractional differential equations
本地全文：下载
作者：Xiaohui Yang ; Yuji Liu
期刊名称：Advances in Difference Equations
印刷版ISSN：1687-1839
电子版ISSN：1687-1847
出版年度：2014
卷号：2014
期号：1
页码：102
DOI：10.1186/1687-1847-2014-102
语种：English
出版社：Hindawi Publishing Corporation
摘要：In this paper, the initial value problems of singular fractional differential equations are discussed. New criteria on the existence and uniqueness of solutions are obtained. The well-known Picard iterative technique is then extended for fractional differential equations which provides computable sequences that converge uniformly to the solution of the problems discussed. We obtain not only the existence and uniqueness of solutions for the problems, but we also establish iterative schemes for uniformly approximating the solutions. Two examples are given to illustrate the main theorems. MSC:34K05, 34A12, 34A40.
关键词：initial value problem ; singular fractional differential equation ; the Riemann-Liouville fractional derivative ; the Caputo fractional derivative ; Picard iterative method