Theorems on certain fractional functional function and derivative

الملخص EN

The aim of this paper is to prove the correctness of the relation I-a I aha (x) = h a (x) for all x e (a, b], 0 < a < 1, after we prove the continuity of the fractional function = (u (x-a)1-a )/(r (a)) + 1/(r (a)) (X – t) f a- 1 f (g(t) )dt in (a,oo), where |ha(x)| < M for all xe (a,oo) and (Me R+, M>0).

The aim of this paper is to prove the correctness of the relation I-a I aha (x) = h a (x) for all x e (a, b], 0 < a < 1, after we prove the continuity of the fractional function = (u (x-a)1-a )/(r (a)) + 1/(r (a)) (X – t) f a- 1 f (g(t) )dt in (a,oo), where |ha(x)| < M for all xe (a,oo) and (Me R+, M>0).