Abstract
In this paper, a new idea of exploring the variable order fractional calculus on the fractal interpolation functions is addressed. The studies of constant order fractional calculus on the fractal functions are generalized to the case of variable order. The Riemann–Liouville variable order fractional integral (/derivative) and the Weyl–Marchaud variable order fractional derivative are investigated over the different kinds of fractal interpolation functions (FIFs). Furthermore, the necessary conditions of variable fractional order p(z) defined on the interval $$[x_0,x_N]$$ are also derived. It is observed that under the derived conditions, both the Riemann–Liouville variable order fractional integral (/derivative) and the Weyl–Marchaud variable order fractional derivative of FIFs are again FIFs interpolating new data set.
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