Existence and Uniqueness of Solutions for the Cauchy-Type Problems of Fractional Differential Equations-Reference-Cited by-同舟云学术

Existence and Uniqueness of Solutions for the Cauchy-Type Problems of Fractional Differential Equations

Published:2010 Issue: Volume:2010 Page:1-15
ISSN:1026-0226
Container-title:Discrete Dynamics in Nature and Society
language:en
Short-container-title:Discrete Dynamics in Nature and Society

Author:

Kou Chunhai¹,Liu Jian¹,Ye Yan²

Affiliation:

1. Department of Applied Mathematics, Donghua University, Shanghai 201620, China

2. College of Information Sciences and Technology, Donghua University, Shanghai 201620, China

Abstract

By using the Banach fixed point theorem and step method, we study the existence and uniqueness of solutions for the Cauchy-type problems of fractional differential equations. Meanwhile, by citing some counterexamples, it is pointed out that there exist a few defects in the proofs of the known results.

Funder

National Natural Science Foundation of China

Publisher

Hindawi Limited

Subject

Modelling and Simulation

Link

http://downloads.hindawi.com/journals/ddns/2010/142175.pdf

Reference28 articles.

1. Fractional differential equations as alternative models to nonlinear differential equations

2. A fractional differential equation for a MEMS viscometer used in the oil industry

3. On fractional order differential equations model for nonlocal epidemics