The first intriguing element for integrating fractal functions and fractional order is the fractal dimension. Fractal sets, fractal functions, and fractal surfaces have non-integer (fractional) fractal dimension, in general. This characteristic has opened up the potential of bridging the two distinct domains of fractal geometry and fractional calculus, see [1–4]. Later, motivated by the merits of fractional calculus, the trend of applying fractional derivative and fractional integral to fractal interpolation functions has gained popularity. One more non-avoidable reason behind this study is the non-differentiable nature of fractal interpolation functions despite they are continuous everywhere. For detailed study on the fractional derivative and fractional integral of fractal functions, interested readers may refer the literature [5–10]. Among the various fractional derivative methods, this chapter concentrates on the Weyl-Marchaud fractional derivative.