HÖLDER Continuity and Box Dimension for the Weyl Fractional Integral
Abstract
In this paper, we investigate the Hölder continuity and the estimate for the box dimension of the Weyl fractional integral of some continuous function f(x), denoted by Wαf(x). We obtain that if f(x) is μorder Hölder continuous, then Wαf(x) is α+μ α+1order Hölder continuous. Moreover, if μ belongs to (0, 1  α), then Wαf(x) is λorder Hölder continuous with λ = α (1μ)(1+α)α2.
 Publication:

Fractals
 Pub Date:
 2020
 DOI:
 10.1142/S0218348X20500322
 Bibcode:
 2020Fract..2850032T
 Keywords:

 Weyl Fractional Integral;
 Hölder Continuity;
 Box dimension