Fuzzy Differential Subordination and Superordination Results Involving the q-Hypergeometric Function and Fractional Calculus Aspects

Alb Lupaş, Alina; Oros, Georgia Irina

doi:10.3390/math10214121

Open AccessArticle

Fuzzy Differential Subordination and Superordination Results Involving the q-Hypergeometric Function and Fractional Calculus Aspects

by

Alina Alb Lupaş

^*,†

and

Georgia Irina Oros

^†

Department of Mathematics and Computer Science, University of Oradea, 1 Universitatii Street, 410087 Oradea, Romania

^*

Author to whom correspondence should be addressed.

^†

These authors contributed equally to this work.

Mathematics 2022, 10(21), 4121; https://doi.org/10.3390/math10214121

Submission received: 14 September 2022 / Revised: 29 October 2022 / Accepted: 2 November 2022 / Published: 4 November 2022

(This article belongs to the Special Issue Fuzzy Logic and Soft Computing—In Memory of Lotfi A. Zadeh)

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Abstract

The concepts of fuzzy differential subordination and superordination were introduced in the geometric function theory as generalizations of the classical notions of differential subordination and superordination. Fractional calculus is combined in the present paper with quantum calculus aspects for obtaining new fuzzy differential subordinations and superordinations. For the investigated fuzzy differential subordinations and superordinations, fuzzy best subordinates and fuzzy best dominants were obtained, respectively. Furthermore, interesting corollaries emerge when using particular functions, frequently involved in research studies due to their geometric properties, as fuzzy best subordinates and fuzzy best dominants. The study is finalized by stating the sandwich-type results connecting the previously proven results.

Keywords: Riemann–Liouville fractional integral; q-hypergeometric function; fuzzy differential subordination; fuzzy differential superordination; fuzzy best dominant; fuzzy best subordinate

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MDPI and ACS Style

Alb Lupaş, A.; Oros, G.I. Fuzzy Differential Subordination and Superordination Results Involving the q-Hypergeometric Function and Fractional Calculus Aspects. Mathematics 2022, 10, 4121. https://doi.org/10.3390/math10214121

AMA Style

Alb Lupaş A, Oros GI. Fuzzy Differential Subordination and Superordination Results Involving the q-Hypergeometric Function and Fractional Calculus Aspects. Mathematics. 2022; 10(21):4121. https://doi.org/10.3390/math10214121

Chicago/Turabian Style

Alb Lupaş, Alina, and Georgia Irina Oros. 2022. "Fuzzy Differential Subordination and Superordination Results Involving the q-Hypergeometric Function and Fractional Calculus Aspects" Mathematics 10, no. 21: 4121. https://doi.org/10.3390/math10214121

APA Style

Alb Lupaş, A., & Oros, G. I. (2022). Fuzzy Differential Subordination and Superordination Results Involving the q-Hypergeometric Function and Fractional Calculus Aspects. Mathematics, 10(21), 4121. https://doi.org/10.3390/math10214121

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Fuzzy Differential Subordination and Superordination Results Involving the q-Hypergeometric Function and Fractional Calculus Aspects

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