Fuzzy Differential Subordination and Superordination Results for Fractional Integral Associated with Dziok-Srivastava Operator

Lupaş, Alina Alb

doi:10.3390/math11143129

Cited by 3 publications

(1 citation statement)

References 42 publications

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“…In addition, fuzzy differential subordinations and fuzzy differential superordinations results were obtained involving the fractional integral of the Dziok-Srivastava operator in [48]. The fractional integral of the Dziok-Srivastava operator could be used for obtaining higher-order fuzzy differential subordinations, following study [49], regarding the classical theory of differential subordination.…”

Section: Discussionmentioning

confidence: 99%

New Results on a Fractional Integral of Extended Dziok–Srivastava Operator Regarding Strong Subordinations and Superordinations

Lupaş

2023

Symmetry

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In 2012, new classes of analytic functions on U×U¯ with coefficient holomorphic functions in U¯ were defined to give a new approach to the concepts of strong differential subordination and strong differential superordination. Using those new classes, the extended Dziok–Srivastava operator is introduced in this paper and, applying fractional integral to the extended Dziok–Srivastava operator, we obtain a new operator Dz−γHmlα1,β1 that was not previously studied using the new approach on strong differential subordinations and superordinations. In the present article, the fractional integral applied to the extended Dziok–Srivastava operator is investigated by applying means of strong differential subordination and superordination theory using the same new classes of analytic functions on U×U¯. Several strong differential subordinations and superordinations concerning the operator Dz−γHmlα1,β1 are established, and the best dominant and best subordinant are given for each strong differential subordination and strong differential superordination, respectively. This operator may have symmetric or asymmetric properties.

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Section: Discussionmentioning

confidence: 99%

New Results on a Fractional Integral of Extended Dziok–Srivastava Operator Regarding Strong Subordinations and Superordinations

Lupaş

2023

Symmetry

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Notes on q-Gamma Operators and Their Extension to Classes of Generalized Distributions

Al-Omari,

Salameh,

Alhazmi

2024

Symmetry

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This paper discusses definitions and properties of q-analogues of the gamma integral operator and its extension to classes of generalized distributions. It introduces q-convolution products, symmetric q-delta sequences and q-quotients of sequences, and establishes certain convolution theorems. The convolution theorems are utilized to accomplish q-equivalence classes of generalized distributions called q-Boehmians. Consequently, the q-gamma operators are therefore extended to the generalized spaces and performed to coincide with the classical integral operator. Further, the generalized q-gamma integral is shown to be linear, sequentially continuous and continuous with respect to some involved convergence equipped with the generalized spaces.

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Certain geometric properties of the fractional integral of the Bessel function of the first kind

Oros,

Bardac-Vlada

2024

MATH

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<abstract><p>This paper revealed new fractional calculus applications of special functions in the geometric function theory. The aim of the study presented here was to introduce and begin the investigations on a new fractional calculus integral operator defined as the fractional integral of order $ \lambda $ for the Bessel function of the first kind. The focus of this research was on obtaining certain geometric properties that give necessary and sufficient univalence conditions for the new fractional calculus operator using the methods associated to differential subordination theory, also referred to as admissible functions theory, developed by Sanford S. Miller and Petru T. Mocanu. The paper discussed, in the proved theorems and corollaries, conditions that the fractional integral of the Bessel function of the first kind must comply in order to be a part of the sets of starlike functions, positive and negative order starlike functions, convex functions, positive and negative order convex functions, and close-to-convex functions, respectively. The geometric properties proved for the fractional integral of the Bessel function of the first kind recommend this function as a useful tool for future developments, both in geometric function theory in general, as well as in differential subordination and superordination theories in particular.</p></abstract>

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Fuzzy Differential Subordination and Superordination Results for Fractional Integral Associated with Dziok-Srivastava Operator

Cited by 3 publications

References 42 publications

New Results on a Fractional Integral of Extended Dziok–Srivastava Operator Regarding Strong Subordinations and Superordinations

New Results on a Fractional Integral of Extended Dziok–Srivastava Operator Regarding Strong Subordinations and Superordinations

Notes on q-Gamma Operators and Their Extension to Classes of Generalized Distributions

Certain geometric properties of the fractional integral of the Bessel function of the first kind

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