Geodesic
Fractional integrals and differentials of variable order in H\"older spaces~$H^{\omega(t,x)}$
Vladikavkazskij matematičeskij žurnal, Tome 12 (2010) no. 4, pp. 3-11

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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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     author = {B. G. Vakulov and E. S. Kochurov},
     title = {Fractional integrals and differentials of variable order in {H\"older} spaces~$H^{\omega(t,x)}$},
     journal = {Vladikavkazskij matemati\v{c}eskij \v{z}urnal},
     pages = {3--11},
     publisher = {mathdoc},
     volume = {12},
     number = {4},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMJ_2010_12_4_a0/}
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B. G. Vakulov; E. S. Kochurov. Fractional integrals and differentials of variable order in H\"older 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/