Priyanka, T. M. C.Serpa, CristinaGowrisankar, A.2025-09-242025-09-242024Priyanka, T. M. C., Serpa, C., & Gowrisankar, A. (2024). a-fractal function with variable parameters: an explicit representation. Fractals – Complex Geometry Patterns and Scaling in Nature and Society, 32(02), 1-12. https://doi.org/10.1142/S0218348X244000850218-348Xhttp://hdl.handle.net/10400.21/22151In this paper, new results on the alpha-fractal function with variable parameters are presented. The Weyl-Marchaud variable order fractional derivative of an alpha-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 alpha-fractal function with variable parameters is evaluated for various intervals in the prescribed domain. Finally, an explicit structure for the alpha-fractal function is provided using the base q representation of numbers.engAlpha-fractal functionVariable parametersFractional derivativeDefinite integralBase representationUIDB/04561/2020research articlehttps://doi.org/10.1142/S0218348X244000851793-6543