Riemann–Liouville Fractional Calculus of Nonlinear Hidden Variable Recurrent Fractal Interpolation Functions Based on Rakotch Contraction

In this paper, we study Riemann–Liouville fractional calculus of nonlinear hidden variable recurrent fractal interpolation function (HVRFIF) constructed based on Rakotch contraction, which is a generalization of Banach contraction. First, we prove that Riemann–Liouville fractional integral and derivative of HVRFIF based on Rakotch contraction are also HVRFIFs based on the same Rakotch contraction. Next, we estimate the upper bounds of the box‐counting dimensions of Riemann–Liouville fractional integral and derivative of HVRFIF based on Rakotch contraction. Finally, we give the graph of Riemann–Liouville fractional integral of HVRFIF based on Rakotch contraction in case α = 0.45.