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Fractal functions based on piecewise continuous functions and box dimension results in Hölder settings
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DOI：10.1016/j.cnsns.2026.110509.png)
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Abstract
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• A new class of fractal functions fBα is introduced via piecewise functions and a family of base functions. • A complete metric space M of continuous piecewise Hölder functions is established for both fixed and varying Hölder exponents. • Fractal functions in M are constructed under uniform and non-uniform Hölder scaling settings. • Bounds for the box dimension of the graph of fBα are derived on subintervals and the whole domain for equally spaced partitions. • Box-dimension estimates are obtained using oscillation and variation properties without requiring equally spaced partitions.
Keywords:
Fractals
Hölder functions
Approximation
Fractal Functions
Oscillation and variation
Box-dimension
28A80
41A05
26A16
41A30
65D10
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