α-FRACTAL FUNCTION WITH VARIABLE PARAMETERS: AN EXPLICIT REPRESENTATION.

In this paper, new results on the α -fractal function with variable parameters are presented. The Weyl–Marchaud variable order fractional derivative of an α -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 α -fractal function with variable parameters is evaluated for various intervals in the prescribed domain. Finally, an explicit structure for the α -fractal function is provided using the base q representation of numbers. [ABSTRACT FROM AUTHOR]