الفهرس 
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Abstract
In this work we are concerned with the existence of a unique solution of some nonlocal, two point, problem of functional integro-differential equation with arbitrary (fractional) orders.
Firstly, in Chapter 2, we are concerned by with the nonlocal (two point)
problem of integro-differential equation of arbitrary (fractional) orders
dx Z 1
= f (t,
dt 0
k(t, s)Dα x(s)ds), t ∈ (0, 1)
with the nonlocal condition
x(τ ) = γ x(ξ), τ ∈ [0, 1) , ξ ∈ (0, 1] , γ = 1.
The existence of a unique solution x ∈ C[0, 1] and dx ∈ C[0, 1] will be proved. Also the existence of a unique absolutely continuous solution , x ∈ AC[0, 1] will
be also proved. Also in L1[0, 1].
Secondly, in Chapter 3, we study the nonlocal (two point) problem of the integro-functional differential equations
dx Z 1
= f (t,
dt 0
k(t, s)g(s, Dα x(s)ds)), t ∈ (0, 1)
with the nonlocal condition
x(τ ) = γ x(ξ), τ ∈ [0, 1) , ξ ∈ (0, 1] , γ = 1.
The existence of a unique solution x ∈ C[0, 1] and dx
∈ C[0, 1] will be
proved.
Also the existence of a unique absolutely continuous solution , x ∈ AC[0, 1]
will be also proved. Also in L1[0, 1].