CONSTRUCTION OF NEW AFFINE AND NON-AFFINE FRACTAL INTERPOLATION FUNCTIONS THROUGH THE WEYL-MARCHAUD DERIVATIVE

This paper investigates the Weyl-Marchaud fractional derivative of affine and non-affine fractal interpolation functions with function scaling factors. The dependence of fractal interpolation function on the scaling factor is mainly explored by choosing the scaling factor as a function instead of a constant. In addition, for some fixed order v, the Weyl-Marchaud fractional derivative of a linear fractal interpolation function is estimated by predefining the fractional derivative values at the end points. Similarly, the Weyl-Marchaud fractional derivative of a a-fractal function is investigated for some fixed order v with additional constraints on the derivative of prescribed continuous function and base function.