The aim of this paper is to prove the correctness of the relation
I I h ( ) = h ( ) for all xÎ(a, b], -
x x
x
a
x
a
a a
a a
0after we prove the
continuity of the fractional function
(x t) f (g(t))dt
( )
1
( )
(x - a) h (x) 1
1-
ò
-
-
G
+
G
=
a
a
a
a a
m
in (a,∞), where |ha(x)| ≤ M
for all xÎ(a,∞) and (MÎR+, M>0).
Keywords: Fractional function, derivative.
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