Theorems on Certain Fractional Function and Derivative
Dr. Ahmed Zain al-Abdin , Maha Abd Al-Wahab

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.