$\alpha$-Differentiable functions in complex plane
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 c...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Samara State Technical University
2020-01-01
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| Series: | Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki |
| Online Access: | http://mi.mathnet.ru/vsgtu1734 |
| Summary: | 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. |
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| ISSN: | 1991-8615 2310-7081 |