On the Variable Order Fractional Calculus Characterization for the Hidden Variable Fractal Interpolation Function

Abstract

In this study, the variable order fractional calculus of the hidden variable fractal interpolation function is explored. It extends the constant order fractional calculus to the case of variable order. The Riemann–Liouville and the Weyl–Marchaud variable order fractional calculus are investigated for hidden variable fractal interpolation function. Moreover, the conditions for the variable fractional order μ on a specified range are also derived. It is observed that, under certain conditions, the Riemann–Liouville and the Weyl–Marchaud variable order fractional calculus of the hidden variable fractal interpolation function are again the hidden variable fractal interpolation functions interpolating the new data set.

Keywords

• hidden variable fractal interpolation function
• variable order
• Riemann–Liouville fractional calculus
• Weyl–Marchaud fractional derivative