Abstract

In this work a class of boundary value problem including fractional differential equa
tion is studied. The existence and uniqueness of solution for a nonlinear fractional
boundary value problem are discussed. This problem includes a nonlinear fractional
differential equation of order α ∈ (0,1] and fractional integral boundary conditions.
In fact we consider the following boundary value problem of fractional differential
equation
c D α y(t) = f(t,y(t))
0 < α < 1, t ∈ J := [0,T] (1)
y(0) + µ
Z
T
0
y(s)ds = y(T),
where
c D α
denotes the Caputo fractional derivative of order α, f : J × R → R is
given function will be specified later and µ ∈ R.
Banach contraction principle and BrowderPoter fixed point theorem will be used
for proving existence and uniqueness of solution for that problem.
