This paper investigates the classical integral of various types of fractal interpolation functions
namely linear fractal interpolation function, α-fractal function and hidden variable fractal …

The goal of this article is to study the box dimension of the mixed Katugampola fractional
integral of two-dimensional continuous functions on [0, 1]×[0, 1]. We prove that the box …

In this paper, we mainly investigate the geometric based relationship between the
Katugampola fractional calculus and a Weierstrass-type function whose graph can be …

Calculating fractal dimension of the graph of a function not simple even for real-valued
functions. While through this paper, our intention is to provide some initial theories for the …

This chapter explores the Katugampola fractional integral of a multivariate vector-valued
function defined on. Alongside, it is shown that the prescribed fractional operator preserves …

In this paper, we rigorously explore (k, h)-Riemann–Liouville fractional integrals applied to
continuous functions defined on closed real intervals. Firstly, we delve into the analytical …

The research object of this paper is the mixed (κ, s)-Riemann–Liouville fractional integral of
bivariate functions on rectangular regions, which is a natural generalization of the fractional …

Barnsley (1986) introduced the concept of fractal interpolation functions (FIFs). Thereafter,
numerous theories have been developed concerning FIFs and their properties. In this article …

Functions of bounded variation have a greater importance in the sense of integrability. This
kind of functions have several known properties such as differentiability, continuity …

This paper consists of two significant aims. The first aim of this paper is to establish the
criteria for the existence of solutions to nonlinear Volterra-Fredholm (VF) fractional integral …