This paper mainly investigates the Riemann–Liouville fractional integral of α α-fractal
function and fractional operator of α α-fractal function that maps the given continuous …

The objective of this paper is to study the box-counting dimension of graphs of fractal
interpolation functions and harmonic functions on the Sierpiński gasket. Firstly, we give …

Fractal interpolation function defined through suitable iterated function system provides a
method to perturb a function f∈ C (I) so as to yield a class of functions f α∈ C (I), where α is …

The box dimension of the graph of non-affine α-fractal interpolation function f α with variable
scaling factors is estimated in the interval [0, 1]. Due to the non-affinity of f α, the behavior of …

In the framework of non-autonomous discrete dynamical systems in metric spaces, we
propose new equilibrium points, called quasi-fixed points, and prove that they play a role …

Fractal interpolation and approximation received a lot of attention in the last thirty years. The
main aim of the current article is to study a fractal trigonometric approximants which …

The box dimension of the graph of non-affine, continuous, nowhere differentiable function f α
which is a fractal analogue of a continuous function f corresponding to a certain iterated …

This article introduces fractal perturbation of rational functions via α-fractal operator and
investigates some approximation theoretic aspects of this new function class, namely, the …

The paper approaches the construction of fractal surfaces of interpolation and approximation
on the basis of a fractal perturbation of any mapping defined on a rectangle. Conditions for …

Let a data set Δ={(ti, yi)∈ R× Y: i= 0, 1,⋯, N} be given, where t 0< t 1< t 2<⋯< t N and Y is a
complete metric space. In this article, fractal interpolation functions (FIFs) on I=[t 0, t N] …