EXISTENCE AND CONTINUATION THEOREMS OF RIEMANN–LIOUVILLE TYPE FRACTIONAL DIFFERENTIAL EQUATIONS-Reference-Cited by-同舟云学术

EXISTENCE AND CONTINUATION THEOREMS OF RIEMANN–LIOUVILLE TYPE FRACTIONAL DIFFERENTIAL EQUATIONS

Published:2012-04 Issue:04 Volume:22 Page:1250077
ISSN:0218-1274
Container-title:International Journal of Bifurcation and Chaos
language:en
Short-container-title:Int. J. Bifurcation Chaos

Author:

KOU CHUNHAI¹,ZHOU HUACHENG¹,LI CHANGPIN²

Affiliation:

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

2. Department of Mathematics, Shanghai University, Shanghai 200444, P. R. China

Abstract

In this paper we study the existence and continuation of solution to the general fractional differential equation (FDE) with Riemann–Liouville derivative. If no confusion appears, we call FDE for brevity. We firstly establish a new local existence theorem. Then, we derive the continuation theorems for the general FDE, which can be regarded as a generalization of the continuation theorems of the ordinary differential equation (ODE). Such continuation theorems for FDE which are first obtained are different from those for the classical ODE. With the help of continuation theorems derived in this paper, several global existence results for FDE are constructed. Some illustrative examples are also given to verify the theoretical results.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Modeling and Simulation,Engineering (miscellaneous)

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218127412500770

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