Title: An uncustomary calculation of the fractal dimension for graph of mixed (k, s)-Riemann-Liouville fractional integral of a bivariate continuous map

Authors: M. Priya; R. Uthayakumar

Addresses: Department of Mathematics, The Gandhigram Rural Institute (Deemed to be University), Gandhigram, Dindigul, Tamil Nadu – 624302, India ' Department of Mathematics, The Gandhigram Rural Institute (Deemed to be University), Gandhigram, Dindigul, Tamil Nadu – 624302, India

Abstract: In our personal to professional survival, the scope of fractional-order filters is very efficient in image processing techniques. It gets a decisive state in science, engineering, and medical disciplines. With this stimulation, we bestowed a generalisation, called as mixed (k, s)-Riemann-Liouville fractional integral [simply, (k, s) - RLFI]. As an application side of fractal graphs and its classic fractal dimension, we incurred the box dimension of the graph of mixed (k, s) - RLFI of a bivariate continuous function defined over [0, 1] × [0, 1]. This work has been derived without applying the customary method. That is, it has been exhibited that the fractal dimension of the graph of this specific fractional integral of a bivariate continuous function is determined whenever the fractal dimension of the graph of the continuous function is known. Except of these works, we have proved the semigroup property of this particular fractional integral for deriving the connection between the box dimension and the Hausdorff dimension. Additionally, some supporting results are built to secure our main target.

Keywords: mixed (k, s)-Riemann-Liouville fractional integral; box dimension; Hausdorff dimension; semigroup property.

DOI: 10.1504/IJANS.2022.130495

International Journal of Applied Nonlinear Science, 2022 Vol.3 No.4, pp.299 - 316

Received: 06 Apr 2022
Accepted: 17 Jul 2022
Published online: 24 Apr 2023 *

Full-text access for editors Full-text access for subscribers Purchase this article Comment on this article