Geodesic
Fractional integrals and differentials of variable order in Hölder spaces $H^{\omega(t,x)}$
Vladikavkazskij matematičeskij žurnal, Tome 12 (2010) no. 4, pp. 3-11 
B. G. Vakulov; E. S. Kochurov. Fractional integrals and differentials of variable order in Hölder spaces $H^{\omega(t,x)}$. Vladikavkazskij matematičeskij žurnal, Tome 12 (2010) no. 4, pp. 3-11. http://geodesic.mathdoc.fr/item/VMJ_2010_12_4_a0/
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     title = {Fractional integrals and differentials of variable order in {H\"older} spaces~$H^{\omega(t,x)}$},
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Voir la notice de l'article provenant de la source Math-Net.Ru

We consider generalized Hölder spaces of functions on the segment of real axis, whose local continuity modulus has a dominant which may vary from a point to point. We establish theorems on the mapping properties of fractional integrals of variable order, from such a variable generalized Hölder space to another one with a “better” dominant, and similar mapping properties of fractional differentials of variable order from such a space into the space with “worse” dominant. Variable order can take values between zero and unity.

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