SMOOTHNESS AND FRACTIONAL INTEGRAL OF HIDDEN VARIABLE RECURRENT FRACTAL INTERPOLATION FUNCTION WITH FUNCTION VERTICAL SCALING FACTORS

Abstract

In this paper, we analyze the smoothness of hidden variable recurrent fractal interpolation function (HVRFIF) with function vertical scaling factors introduced in Yun [Hidden variable recurrent fractal interpolation function with four function contractivity factors, Fractals 27(7) (2019) 950113] and study on fractional integral of bivariable HVRFIF by using its smoothness. To do it, firstly, we analyze the smoothness of one variable HVRFIF and give the result of smoothness of bivariable HVRFIF. Next, we show that partial and mixed Riemann–Liouville fractional integrals of the bivariable HVRFIF are HVRFIFs.