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α-Fractal Function With Variable Parameters: An Explicit Representation

Author

Listed:
  • T. M. C. PRIYANKA

    (Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore 632 014, Tamil Nadu, India)

  • C. SERPA

    (ISEL — Instituto Superior de Engenharia de Lisboa, Centro de Matemática Aplicações Fundamentais e Investigação Operacional, Faculdade de Ciências, Universidade de Lisboa, 1749-016 Lisbon, Portugal)

  • A. GOWRISANKAR

    (Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore 632 014, Tamil Nadu, India)

Abstract

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.

Suggested Citation

  • T. M. C. Priyanka & C. Serpa & A. Gowrisankar, 2024. "α-Fractal Function With Variable Parameters: An Explicit Representation," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 32(02), pages 1-12.
    • Handle: RePEc:wsi:fracta:v:32:y:2024:i:02:n:s0218348x24400085
    DOI: 10.1142/S0218348X24400085
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