Localized and Local Derivatives of Fractional Order of Functions with a Given Modulus of Continuity
DOI:
https://doi.org/10.52575/2687-0959-2024-56-4-296-313Keywords:
Localized Fractional Derivative, Local Fractional Derivative, Modulus of Continuity of a function, IsomorphismAbstract
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.
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