What question did this study set out to answer?

The aim is to investigate the Riemann–Liouville fractional calculus of HVRFIF constructed using Rakotch contraction.

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February 21, 2026Open Access

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

Key Points

The aim is to investigate the Riemann–Liouville fractional calculus of HVRFIF constructed using Rakotch contraction.
Proved HVRFIF properties of Riemann–Liouville fractional integral and derivative.
Estimated upper bounds of box-counting dimensions for Riemann–Liouville fractional forms.
Presented graph of HVRFIF under fractional integral conditions.
New HVRFIFs retain their characteristics under fractional calculus operations.
Upper bounds for box-counting dimensions were successfully estimated.
Visual representation of the HVRFIF’s fractional integral provided findings for α = 0.45.

Abstract

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.

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

Key Points

Abstract

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