An extensive note on various fractional-order type operators and some of their effects to certain holomorphic functions
Keywords:
complex plane, holomorphic function, series expansion, fractional-order calculus, operators in certain domains, argument propertiesAbstract
The aim of this paper is to present background information in relation with some fractional-order type operators in the complex plane, which is designed by the fractional-order derivative operator(s). Next we state various implications of that operator and then we show some interesting-special results of those applications.
References
Abad, Julio, and Javier Sesma. "Buchholz polynomials: a family of polynomials relating solutions of confluent hypergeometric and Bessel equations." J. Comput. Appl. Math. 101, no. 1-2 (1999): 237-241.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Abdulnaby, Zainab E., Rabha W. Ibrahim, and Adam Kilicman. "On boundedness and compactness of a generalized Srivastava-Owa fractional derivative operator." J. King Saud Univ. Sci. 30, no. 2, (2018): 153-157.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Abramowitz, Milton, and Irene A. Stegun, Confluent Hypergeometric Functions in Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables. New York: John Wiley and Sons, 1972.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Altıntas, Osman, Hüseyin Irmak, and Hari Mohan Srivastava. "Fractional calculus and certain starlike functions with negative coefficients." Comput. Math. Appl. 30, no. 2 (1995): 9-15.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Ch’ên, Ming Po, and Ih Lan. "On certain inequalities for some regular functions defined on the unit disc." Bull. Austral. Math. Soc. 35, no. 3 (1987): 387-396.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Ch’ên, Ming Po, Hüseyin Irmak, and Hari Mohan Srivastava. "Some multivalent functions with negative coefficients defined by using a differential operator." PanAmer. Math. J. 6, no. 2 (1996): 55-64.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Debnath, Lokenath. "A brief historical introduction to fractional calculus." Internat. J. Math. Ed. Sci. Tech. 35, no. 4 (2004): 487-501.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Duren, Peter L. Univalent Functions Vol. 239 of A series of Compehensive Studies in Mathematics. New York, Berlin, Heilderberg and Tokyo: Springer-Verlag, 1983.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Grozdev, Sava. "On the appearance of the fractional calculus." J. Theoret. Appl. Mech. 27, no. 3 (1997): 3,11-20.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Ibrahim, Rabha W., and Maslina Darus. "Integral means of univalent solution for fractional differential equation." Applied Mathematics. 3, no. 6 (2012): Article ID: 20286.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Irmak, Hüseyin. "A variety of multivalently analytic functions with complex coefficients and some argument properties of their applications." Punjab Univ. J. Math. (Lahore) 53, no. 6 (2021): 367-376.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Irmak, Hüseyin, and Olga Engel. "Some results concerning the Tremblay operator and some of its applications to certain analytic functions." Acta Univ. Sapientiae Math. 11, no. 2 (2019): 296-305.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Irmak, Hüseyin. "Certain basic information related to the Tremblay operator and some applications in connection therewith." Gen. Math. 27, no. 2 (2019): 13-21.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Irmak, Hüseyin. "Notes on various operators of fractional calculus and some of their implications for certain analytic functions." Stud. Univ. Babes-Bolyai Math. (Accepted, 2021).
##plugins.generic.googleScholarLinks.settings.viewInGS##
Irmak, Hüseyin. "Characterizations of some fractional-order operators in complex domains and their extensive implications to certain analytic functions." Ann. Univ. Craiova, Mat. Comput. Sci. Ser. 48, no. 2 (2021), 349-357.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Jack, I.S. "Functions starlike and convex of order alpha." J. London Math. Soc. (2) 3 (2) (1971): 469-474.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Khan, Muhammad Bilal, et. al. "LR-Preinvex interval-valued functions and Riemann-Liouville fractional integral inequalities." Fractal Fract. 5, no. 4, (2021): Paper no. 243.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Khan, Muhammad Bilal, et. al. "New Hermite-Hadamard inequalities in fuzzyinterval fractional calculus and related inequalities. " Symmetry 13, no. 4, (2021): Paper no. 673.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Khan, Muhammad Bilal, et. al. "New fuzzy-interval inequalities in fuzzy-interval fractional calculus by means of fuzzy order relation." AIMS Math. 6, no. 10 (2021): 10964-10988.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Lecko, Adam, and Agnieszka Wisniowska. "Geometric properties of subclasses of starlike functions." J. Comput. Appl. Math. 155, no. 2 (2003): 383-387.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Mishra, Akshaya Kumar, and Priyabrat Gochhayat. "Applications of Owa-Srivastava operator to the class of k-uniformly convex functions." Fract. Calc. Appl. Anal. 9, no. 4 (2006): 323-331.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Miller, Sanford S., and Petru T. Mocanu. Differential Subordinations, Theory and Applications. Pure and applied mathematics: A Series of Monograps and Textbooks New York: CRC Press, 2000.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Noor, Khalida Inayat, Rashid Murtaza, and Janusz Sokół. "Some new subclasses of analytic functions defined by Srivastava-Owa-Ruscheweyh fractional derivative operator." Kyungpook Math. J. 57, no. 1 (2017): 109-124.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Nunokawa, Mamoru. "On the theory of multivalent functions." Tsukuba J. Math. 11, no. 2 (1987): 273-286.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Owa, Shigeyoshi. "On the distortion theorems. I." Kyungpook Math. J. 18, no. 1 (1978): 53-59.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Ross, Bertram. "Origins of fractional calculus and some applications." Internat. J. Math. Statist. Sci. 1, no. 1 (1992): 21-34.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Sana, Gul, et. al. "Harmonically convex fuzzy-interval-valued functions and fuzzyinterval Riemann-Liouville fractional integral inequalities." Inter. J. Comput. Intel. Syst. 14, no. 1 (2021): 1809-1822.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Srivastava, Hari M., and Shigeyoshi Owa. Univalent functions, fractional calculus and their applications. New york, Chieschester, Brisbane, Toronto: Halsted Press: John Wiley and Sons, 1989.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Srivastava, Hari Mohan. "Fractional-order derivatives and integrals: introductory overview and recent developments." Kyungpook Math. J. 60, no. 1 (2020): 73-116.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Tremblay, R. "Une Contribution é la théorie de la dérivée fractionnaire." Ph.D. thesis, Université Laval, Québec, Canada, 1974. Cited on 8.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2022 Wydawnictwo Naukowe Uniwersytetu Pedagogicznego
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
