Variable order fractional calculus on \(\alpha\)-fractal functions. (English) Zbl 07822484
Summary: 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.
MSC:
| 28A80 | Fractals |
| 26A33 | Fractional derivatives and integrals |
| 41A05 | Interpolation in approximation theory |
Keywords:
\(\alpha\)-fractal function; variable order; Riemann-Liouville fractional calculus; Weyl-Marchaud fractional derivativeReferences:
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