In many instances, the first derivative of the functional representation f(x) will fail to exist (Mandelbrot, 1987). When this happens, it is important to develop an appropriate language to describe these minute finer roughness and irregularities of the geometric objects. This paper attempts to develop the calculus of fractional derivatives for this purpose. Local approximations to functional values by fractional derivatives provide finer and better estimate than the global approximations represented by power series e.g Mclaurin’s series. Fractional derivatives incorporate information on the fluctuations and irregularities near the true functional values, hence, attaining greater precision.