The relationship between the order of \((k, s)\)-Riemann-Liouville fractional integral and the fractal dimensions of a fractal function (Q2692632)

This paper explores the relationship between the fractal dimension of the graph of the \((k, s)\)-Riemann-Liouville fractional integral and the order of the fractional integral for the well-known fractal function, the Weierstrass function. The authors have investigated several fractal dimensions, including the box dimension, packing dimension, and K-dimension, and establish connections between them. The obtained results are demonstrated by varying the order of the fractional integral, and supporting evidence is derived through graphical representations of the related fractal dimensions. Through their analysis, they have uncovered several important insights into the relationship between fractal dimensions and fractional integrals, shedding new light on the properties of these functions. This study provides valuable contributions to the field of fractal geometry and has the potential to inform future research in this area.