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

Abstract

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 [Formula: see text], 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 [Formula: see text]-fractal function is investigated for some fixed order [Formula: see text] with additional constraints on the derivative of prescribed continuous function and base function.