Fractional Calculus for Multivariate Vector-Valued Function and Fractal Function

Abstract

AbstractThis chapter explores the Katugampola fractional integral of a multivariate vector-valued function defined on \(\mathbb {R}^n\). Alongside, it is shown that the prescribed fractional operator preserves some analytical properties of the original function like continuity and boundedness. Further, this chapter discusses applying one of the fractional calculus formulations called the Weyl-Marchaud fractional derivative on the quadratic fractal interpolation function. The quadratic fractal interpolation function with variable scaling factors has been chosen for the study to elucidate the influence of scaling factors as variables on the fractal functions. By prescribing the initial conditions to the quadratic fractal interpolation function, its fractional derivative is analyzed.