In this paper, the Weyl–Marchaud fractional derivative of various fractal interpolation functions (FIFs) like linear FIF, quadratic FIF, hidden variable FIF and α-FIF is investigated. Further, the fractal dimension of the quadratic FIF is estimated and it is compared with the order of the Weyl–Marchaud fractional derivative. Besides, this paper shows that the Weyl–Marchaud fractional derivative of all FIFs is again FIFs if the order of the fractional derivative meets the necessary condition.

中文翻译：

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具有分形维数的分形插值函数类型的WEYL-MARCHAUD分数导数分析

在本文中，线性 FIF、二次 FIF、隐变量 FIF 和α-FIF 被调查。此外，估计二次 FIF 的分形维数，并将其与 Weyl-Marchaud 分数导数的阶数进行比较。此外，本文表明，如果分数导数的阶满足必要条件，则所有 FIF 的 Weyl-Marchaud 分数导数仍然是 FIF。