Characteristics of a Subclass of Analytic Functions Introduced by Using a Fractional Integral Operator
DOI:
https://doi.org/10.15377/2409-5761.2021.08.5Keywords:
Starlikeness, Extreme points, Analytic functions, Coefficient bounds, differential operatorAbstract
We define a new class of analytic functions Dm,n (λ,δ,µ,α,β) on the open unit disc using the fractional integral associated with a linear differential operator and investigate characteristics of this class: extreme points, distortion bounds, radii of close-to-convexity, starlikeness and convexity.
Downloads
References
Zhou SS, Rashid S, Parveen S, Akdemir AO, Hammouch Z. New computations for extended weighted functionals within the Hilfer generalized proportional fractional integral operators, AIMS Mathematics 2021; 6(5): 4507–4525. DOI: 10.3934/math.2021267. DOI: https://doi.org/10.3934/math.2021267
Rashid S, Ashraf R, Bayones FS. A novel treatment of fuzzy fractional Swift–Hohenberg equation for a hybrid transform within the fractional derivative operator, Fractal and Fractional 2021; 5(4): 209. https://doi.org/10.3390/fractalfract5040209. DOI: https://doi.org/10.3390/fractalfract5040209
Alqudah MA, Ashraf R, Rashid S, Singh J, Hammouch Z, Abdeljawad T. Novel numerical investigations of fuzzy Cauchy reaction–diffusion models via generalized fuzzy fractional derivative operators, Fractal and Fractional, 2021; 5(4): 151. https://doi.org/10.3390/fractalfract5040151. DOI: https://doi.org/10.3390/fractalfract5040151
Al-Qurashi M, Rashid S, Jarad F, Tahir M, Alsharif AM. New computations for the two-mode version of the fractional Zakharov-Kuznetsov model in plasma fluid by means of the Shehu decomposition method, AIMS Mathematics, 2022; 7(2): 2044-2060. doi:10.3934/math.2022117. DOI: https://doi.org/10.3934/math.2022117
Rashid S, Hammouch Z, Aydi H, Ahmad AG, Alsharif AM. Novel computations of the time-fractional Fisher’s model via generalized fractional integral operators by means of the Elzaki Transform, Fractal and Fractional, 2021; 5(3): 94. https://doi.org/10.3390/fractalfract5030094. DOI: https://doi.org/10.3390/fractalfract5030094
Rashid S, Khalid A, Bazighifan O, Oros GI. New modifications of integral inequalities via -Convexity pertaining to fractional calculus and their applications, Mathematics 2021; 9(15): 1753; https://doi.org/10.3390/math9151753. DOI: https://doi.org/10.3390/math9151753
Almalahi MA, Bazighifan O, Panchal SK, Askar SS, Oros GI. Analytical study of two nonlinear coupled hybrid systems involving generalized Hilfer fractional operators, Fractal and Fractional, 2021; 5(4): 178; https://doi.org/10.3390/fractalfract5040178. DOI: https://doi.org/10.3390/fractalfract5040178
Rashid S, Ashraf R, Akdemir AO, Alqudah MA, Abdeljawad T, Mohamed MS. Analytic fuzzy formulation of a time-fractional Fornberg–Whitham model with Power and Mittag–Leffler kernels, Fractal and Fractional, 2021; 5(3): 113. https://doi.org/10.3390/fractalfract5030113. DOI: https://doi.org/10.3390/fractalfract5030113
Lupas AA, Catas A. An application of the principle of differential subordination to analytic functions involving Atangana-Baleanu fractional integral of Bessel functions, Symmetry, 2021; 13: 971. https://doi.org/10.3390/sym13060971. DOI: https://doi.org/10.3390/sym13060971
Srivastava HM, Bansal M, Harjule P. A study of fractional integral operators involving a certain generalized multi-index Mittag-Leffler function, Math. Meth. Appl. Sci., 2018; 1-14. DOI: https://doi.org/10.1002/mma.5122
Ghanim F, Al-Janaby HF. An analytical study on Mittag-Leffler-confluent hypergeometric functions with fractional integral operator. Math. Methods Appl. Sci., 2021; 44(5): 3605-3614. DOI: https://doi.org/10.1002/mma.6966
Ghanim F, Al-Janaby HF, Bazighifan O. Some new extensions on fractional differential and integral properties for Mittag-Leffler confluent hypergeometric function, Fractal and Fractional, 2021; 5: 143. DOI: https://doi.org/10.3390/fractalfract5040143
Lupas AA, Cioban M. On a subclass of analytic functions defined by a fractional integral operator, International Conference on Mathematics, Informatics and Information Technologies, 19-21 April, 2018; B l i, Republica Moldova, 8-14.
Lupas AA. A subclass of analytic functions defined by a fractional integral operator, J. Comput. Anal. Appl., 2019; 27(3): 502-505.
Cho NE, Aouf MK, Srivastava R. The principle of differential subordination and its application to analytic and p-valent functions defined by a generalized fractional differintegral operator, Symmetry 2019; 11: 1083. DOI: https://doi.org/10.3390/sym11091083
Lupas AA. Inequalities for Analytic Functions Defined by a Fractional Integral Operator. In Frontiers in Functional Equations and Analytic Inequalities; Anastassiou, G., Rassias, J., Eds.; Springer: Berlin/Heidelberg, Germany, 2020; 731-745. DOI: https://doi.org/10.1007/978-3-030-28950-8_36
Lupas AA. About a subclass of analytic functions defined by a fractional integral operator, Montes Taurus J. Pure Appl. Math. 2021; 3(3): 200-210.
Lupas AA. New Applications of the Fractional Integral on Analytic Functions, Symmetry 2021; 13(3): 423; https://doi.org/10.3390/sym13030423 DOI: https://doi.org/10.3390/sym13030423
Lupas AA, Oros GI. Differential Subordination and Superordination Results Using Fractional Integral of Confluent Hypergeometric Function, Symmetry 2021; 13(2): 327; https://doi.org/10.3390/sym13020327 DOI: https://doi.org/10.3390/sym13020327
Lupas AA, Oros GI. On special differential subordinations using fractional integral of S l gean and Ruscheweyh operators, Symmetry 2021; 13(9): 1553. https://doi.org/10.3390/sym13091553 DOI: https://doi.org/10.3390/sym13091553
Oros GI. Fuzzy differential subordinations obtained using a hypergeometric integral operator, Mathematics, 2021; 9(20): 2539. https://doi.org/10.3390/math9202539 DOI: https://doi.org/10.3390/math9202539
El-Deeb SM, Lupas AA. Fuzzy Differential Subordinations Connected with Convolution, Studia Universitatis Babe -Bolyai Mathematica, accepted 2020. DOI: https://doi.org/10.21136/MB.2020.0159-19
Cho NE, Aouf AMK. Some applications of fractional calculus operators to a certain subclass of analytic functions with negative coefficients, Tr. J. of Mathematics, 1996; 20: 553-562.
Downloads
Published
Issue
Section
License
Copyright (c) 2021 Alina Alb Lupas
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
All the published articles are licensed under the terms of the Creative Commons Attribution Non-Commercial License (CC BY-NC 4.0) which permits unrestricted, non-commercial use, distribution and reproduction in any medium, provided the work is properly cited.
