An uncustomary calculation of the fractal dimension for graph of mixed (k, s)-Riemann-Liouville fractional integral of a bivariate continuous map. (14th April 2023)

• Record Type: Journal Article
• Authors: Priya, M.; Uthayakumar, R.
• Is Part Of: International journal of applied nonlinear science. Volume 3:Number 4(2022)
• Page Start: 299
• Page End: 316
• Publication Date: 2023-04-14
• Subjects: mixed (k, s)-Riemann-Liouville fractional integral -- box dimension -- Hausdorff dimension -- semigroup property; Science -- Mathematical models -- Periodicals; Engineering -- Mathematical models -- Periodicals; Nonlinear theories -- Periodicals; 501.5118
• Languages: English
• ISSNs: 1752-2862

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.