Weyl-Marchaud fractional derivative of a vector valued fractal interpolation function with function contractivity factors

This article explores the idea of Weyl-Marchaud fractional derivative on the vector-valued fractal interpolation function with function contractivity factors. Initially, the Weyl-Marchaud fractional derivative of a hidden variable fractal interpolation function (HFIF) with function contractivity factors is differentiated and proved as HFIF when the fractional order meets the necessary condition. Further, a new HFIF called the quadratic hidden variable fractal interpolation function (QHFIF) is introduced and its Weyl-Marchaud fractional derivative is investigated with function contractivity factors which generalizes the fractional derivative of QHFIF with constant contractivity factors. The variables in the HFIF have been chosen as functions that influence the fractal characteristics of the fractal functions, in order to maximize their effectiveness on fractal functions.