The shape and dimension of the fractal function have been significantly influenced by the scaling factor. This paper investigatedthe fractional integral of the nonlinear fractal interpolation function corresponding to the iterated function systems employed by Rakotchcontraction. We demonstrated how the scaling factors affect the flexibility of fractal functions and their different fractional orders of theRiemann fractional integral using certain numerical examples. The potentiality application of Rakotch contraction of fractal functiontheory 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.

Climate change is an inevitable and important problem faced worldwide. Around the world, many researchers are doing research work on climate change with different factors. The authors of this study have used the fractal dimension to analyze the $41$ years of climate change in India, from $1981$ to $2021$. The meteorological parameters, surface pressure, temperature, wind speed, and precipitation of $45$ places in India were investigated for this research study. Each parameter was individually examined. As a result of this research, the mean average fractal dimension value of all parameters was acquired from $1.184$ to $1.198$. It was found that all the parameters within the data set, had a long-term persistence behavior. With these values, a suggestion for the prediction of the parameters was proposed. The results of the integrated analysis of these parameters showed that, with the exception of a location, all landscapes had a feature that precipitation increased with the temperature. Moreover, with the exception of two landscapes (the island and the frosty mountains), all areas received heavy rainfall during periods of low wind. Thus, this study contributes to a better understanding of the fractal aspects of climate change and the complexity of irregularity and the classification of weather characteristics.