Journal of Pure and Applied Mathematics: Advances and ApplicationsAuthor's: ZHIQIANG ZHOU and HONGYING WU
Pages: [85] - [103]
Received Date: October 23, 2011, Revised November 6, 2011
Submitted by: Jingtang Ma.
In this paper, we discuss existence and uniqueness of solutions of
initial-value problems for nonlinear fractional differential equations
with Riemann-Liouville differential derivatives. In principle, we may
reduce such an equation to an integral equation with regular or weakly
singular kernel and then apply to it basic techniques of fixed points
theorems. Proceeding in this direction, we present a list of theorems
of existence and uniqueness of continuous solutions on 
or 
and give some examples to illustrate that
these theorems can be used directly as a method for solving fractional
differential equations.
fractional differential equation, Riemann-Liouville derivative, existence and uniqueness.
