Abstract
The calculus of the mixed Weyl–Marchaud fractional derivative has been investigated in this paper. We prove that the mixed Weyl–Marchaud fractional derivative of bivariate fractal interpolation functions (FIFs) is still bivariate FIFs. It is proved that the upper box dimension of the mixed Weyl–Marchaud fractional derivative having fractional order [Formula: see text] of a continuous function which satisfies [Formula: see text]-Hölder condition is no more than [Formula: see text] when [Formula: see text], [Formula: see text], [Formula: see text], which reveals an important phenomenon about linearly increasing effect of dimension of the mixed Weyl–Marchaud fractional derivative. Furthermore, we deduce box dimension of the graph of the mixed Weyl–Marchaud fractional derivative of a continuous function which is defined on a rectangular region in [Formula: see text] and also, we analyze that the mixed Weyl–Marchaud fractional derivative of a function preserves some basic properties such as continuity, bounded variation and boundedness. The results are new and compliment the existing ones.
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