Fractional integral approach on nonlinear fractal function and its application

Abstract

The shape and dimension of the fractal function have been significantly influenced by the scaling factor. This paper investigated the fractional integral of the nonlinear fractal interpolation function corresponding to the iterated function systems employed by Rakotch contraction. We demonstrated how the scaling factors affect the flexibility of fractal functions and their different fractional orders of the Riemann fractional integral using certain numerical examples. The potentiality application of Rakotch contraction of fractal function theory was elucidated based on a comparative analysis of the irregularity relaxation process. Moreover, a reconstitution of epidemic curves from the perspective of a nonlinear fractal interpolation function was presented, and a comparison between the graphs of linear and nonlinear fractal functions was discussed.