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This article is cited in 2 scientific papers (total in 2 papers)
Short Communication
Differential Equations and Mathematical Physics
$\alpha$-Differentiable functions in complex plane
R. Pashaeia, A. Pishkoob, M. S. Asgaria, D. Ebrahimi Baghaa a Islamic Azad University, Central Tehran Branch, Tehran, Iran
b Nuclear Science and Technology Research Institute, Tehran, Iran
(published under the terms of the Creative Commons Attribution 4.0 International License)
Abstract:
In this paper, the conformable fractional derivative of order $\alpha$ is defined in complex plane.
Regarding to multi-valued function $z^{1-\alpha}$, we obtain fractional Cauchy–Riemann equations which in case of $\alpha=1$ give classical Cauchy–Riemann equations.
The properties relating to complex conformable fractional derivative of certain functions in complex plane have been considered.
Then, we discuss about two complex conformable differential equations and solutions with their Riemann surfaces.
For some values of order of derivative, $\alpha$, we compare their plots.
Keywords:
conformable fractional derivative, Cauchy–Riemann equations, limit based fractional derivative.
Received: August 9, 2019 Revised: February 19, 2020 Accepted: March 16, 2020 First online: May 25, 2020
Citation:
R. Pashaei, A. Pishkoo, M. S. Asgari, D. Ebrahimi Bagha, “$\alpha$-Differentiable functions in complex plane”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 24:2 (2020), 379–389
Linking options:
https://www.mathnet.ru/eng/vsgtu1734 https://www.mathnet.ru/eng/vsgtu/v224/i2/p379
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