Abstract:
The article considers localized derivatives of the Riemann – Liouville, Marchaud type and localized integrals of the Riemann – Liouville type of functions with a given modulus of continuity. For the localized integral, a left inverse operator is introduced and a theorem on isomorphism in Holder spaces is proved. Conditions are obtained that connect the modulus of continuity of a function, the boundedness of the Wiener p-variation and the fulfillment of the Holder condition. The possibility of representing a Holder function as a difference of two almost increasing Holder functions is proved.
Keywords:localized Fractional Derivative, local Fractional Derivative, modulus of Continuity of a function, isomorphism.
