Riemann Liouville fractional integral of hidden variable fractal interpolation function

Abstract

Abstract In this paper, we study Riemann Liouville fractional integral of hidden variable fractal interpolation function (HVFIF) constructed by functions whose Lipschitz exponents are in (0, 1]. Firstly, we present a construction of HVFIF using functions of which Lipschitz exponents are in (0, 1], so that the Riemann Liouville fractional integral of the HVFIF becomes a fractal interpolation function, and give an example where Lipschitz exponents of functions of IFS are in (0, 1]. Secondly, we prove that the Riemann Liouville fractional integral is also a HVFIF with function vertical scaling factors defined newly. Finally, we give the graphs of 0.8- and 0.2-order fractional integrals of the HVFIFs constructed in the above example.