Variable order fractional calculus on α-fractal functions

This study interrogates the variable order fractional calculus of the non-linear fractal interpolation function which is generalized to the case of constant order fractional calculus. The Riemann-Liouville variable order fractional integral (and derivative) and the Weyl-Marchaud variable order fractional derivative of alpha-fractal function is discussed in this paper. Additionally, the necessary conditions for the variable order xi(x) defined on the domain [x(0), x(N)] are also investigated. It is observed that, under the derived conditions, both the fractional calculus and the fractional derivative of non-affine fractal interpolation function with variable order are again non-affine fractal interpolation function.