α-FRACTAL FUNCTION WITH VARIABLE PARAMETERS: AN EXPLICIT REPRESENTATION

T. M. C. Priyanka (), C. Serpa () and A. Gowrisankar
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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

FRACTALS (fractals), 2024, vol. 32, issue 02, 1-12

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.

Keywords: α-Fractal Function; Variable Parameters; Fractional Derivative; Definite Integral; Base Representation (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1142/S0218348X24400085

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