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Theory and Modern Applications

Table 2 Proposed y -directional fractional mask

From: A new construction of a fractional derivative mask for image edge analysis based on Riemann-Liouville fractional derivative

\(\frac{2\alpha\sqrt{8^{\alpha}}}{8\Gamma(1-\alpha)}\)

\(\frac{2\alpha \sqrt{5^{\alpha}}}{5\Gamma(1-\alpha)}\)

\(\frac{2\alpha\sqrt{4^{\alpha}}}{4\Gamma(1-\alpha)}\)

\(\frac{2\alpha\sqrt{5^{\alpha}}}{5\Gamma(1-\alpha )}\)

\(\frac{2\alpha\sqrt{8^{\alpha}}}{8\Gamma(1-\alpha)}\)

\(\frac{\alpha\sqrt{5^{\alpha}}}{5\Gamma(1-\alpha)}\)

\(\frac{\alpha\sqrt {2^{\alpha}}}{2\Gamma(1-\alpha)}\)

\(\frac{\alpha}{\Gamma(1-\alpha)}\)

\(\frac{\alpha\sqrt{2^{\alpha}}}{2\Gamma(1-\alpha)}\)

\(\frac{\alpha\sqrt {5^{\alpha}}}{5\Gamma(1-\alpha)}\)

0

0

0

0

0

\(\frac{-\alpha\sqrt{5^{\alpha}}}{5\Gamma(1-\alpha)}\)

\(\frac{-\alpha \sqrt{2^{\alpha}}}{2\Gamma(1-\alpha)}\)

\(\frac{-\alpha}{\Gamma(1-\alpha )}\)

\(\frac{-\alpha\sqrt{2^{\alpha}}}{2\Gamma(1-\alpha)}\)

\(\frac {-\alpha\sqrt{5^{\alpha}}}{5\Gamma(1-\alpha)}\)

\(\frac{-2\alpha\sqrt{8^{\alpha}}}{8\Gamma(1-\alpha)}\)

\(\frac{-2\alpha \sqrt{5^{\alpha}}}{5\Gamma(1-\alpha)}\)

\(\frac{-2\alpha\sqrt{4^{\alpha}}}{4\Gamma(1-\alpha)}\)

\(\frac{-2\alpha\sqrt{5^{\alpha}}}{5\Gamma (1-\alpha)}\)

\(\frac{-2\alpha\sqrt{8^{\alpha}}}{8\Gamma(1-\alpha)}\)