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Study on fractal interpolation functions and fractional caclulus is of great significance in practical applications.
Fractal interpolation functions are powerful tools to model very complex and irregular objects, such as seismic data and electrocardiograms, whereas fractional calculus have been widely applied in practical problems, such as viscoelastic theory in mechanics, biochemistry, finance and so on.
Therefore, there are many mathematicians who have been studying about fractal interpolation functions and their fractional calculus.
At the faculty of mathematics of
We show that not only fractional integral but also Riemann-Liouville fractional derivative of a hidden variable recurrent fractal interpolation function with function contractivity factors is a hidden variable recurrent fractal interpolation function with function contractivity factors and derive the relationship between the orders of fractional calculus and their box-counting dimensions.
These results were published in "Chaos, Solitons and Fractals"(156, 2022) under the title of "Riemann-Liouville fractional derivatives of hidden variable recurrent fractal interpolation functions with function scaling factors and box dimension" (https://doi.org/10.1016/j.chaos.2022.111793).