α-FRACTAL FUNCTION WITH VARIABLE PARAMETERS: AN EXPLICIT REPRESENTATION

Abstract

In this paper, new results on the [Formula: see text]-fractal function with variable parameters are presented. The Weyl–Marchaud variable order fractional derivative of an [Formula: see text]-fractal function with variable parameters is examined by imposing certain conditions on the scaling factors. Following the investigation of fractional derivative, the definite integral of the [Formula: see text]-fractal function with variable parameters is evaluated for various intervals in the prescribed domain. Finally, an explicit structure for the [Formula: see text]-fractal function is provided using the base [Formula: see text] representation of numbers.