Picard iterative processes for initial value problems of singular fractional differential equations

被引：0
|
作者：
Xiaohui Yang
Yuji Liu
机构：
[1] Guangdong Police College,Department of Computers
[2] Guangdong University of Finance and Economics,Department of Mathematics
来源：
Advances in Difference Equations | / 2014卷
关键词：
initial value problem; singular fractional differential equation; the Riemann-Liouville fractional derivative; the Caputo fractional derivative; Picard iterative method;
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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.
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