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Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]:
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Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 2020, Volume 24, Number 2, Pages 379–389 (Mi vsgtu1734)  

This article is cited in 1 scientific paper (total in 1 paper)

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

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
* Author to whom correspondence should be addressed

DOI: https://doi.org/10.14498/vsgtu1734

Full text: PDF file (1931 kB) (published under the terms of the Creative Commons Attribution 4.0 International License)
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Bibliographic databases:

UDC: 517.548
MSC: 26A33, 32A10
Received: August 9, 2019
Revised: February 19, 2020
Accepted: March 16, 2020
First online: May 25, 2020
Language:

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

Citation in format AMSBIB
\Bibitem{PasPisAsg20}
\by R.~Pashaei, A.~Pishkoo, M.~S.~Asgari, D.~Ebrahimi Bagha
\paper $\alpha$-Differentiable functions in complex plane
\jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]
\yr 2020
\vol 24
\issue 2
\pages 379--389
\mathnet{http://mi.mathnet.ru/vsgtu1734}
\crossref{https://doi.org/10.14498/vsgtu1734}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000555617100009}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Martinez F., Martinez I., Kaabar M.K.A., Paredes S., “New Results on Complex Conformable Integral”, AIMS Math., 5:6 (2020), 7695–7710  crossref  mathscinet  isi  scopus
  • Вестник Самарского государственного технического университета. Серия: Физико-математические науки
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