Applications of differential subordinations involving a generalized fractional differintegral operator

Zayed, H. M.; Bulboacă, Teodor

doi:10.1186/s13660-019-2198-0

Cited by 8 publications

(3 citation statements)

References 21 publications

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“…The topic continues to spark fresh ideas and recent papers present interesting outcome. Certain classes of admissible functions are described and particular uses of third-order differential subordination for p-valent functions associated with generalized fractional differintegral operator are examined in [17] using the third-order differential subordination fundamental results. Using the same idea of defining suitable classes of admissible functions generates interesting results involving a generalized operator in [18] and concerning special functions in [19,20].…”

Section: Definition 3 ([3]mentioning

confidence: 99%

New Applications of Gaussian Hypergeometric Function for Developments on Third-Order Differential Subordinations

Oros

Preluca

2023

Symmetry

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The main objective of this paper is to present classical second-order differential subordination knowledge extended in this study to include new results regarding third-order differential subordinations. The focus of this study is on the main problems examined by differential subordination theory. Hence, the new results obtained here reveal techniques for identifying dominants and the best dominant of certain third-order differential subordinations. Another aspect of novelty is the new application of the Gaussian hypergeometric function. Novel third-order differential subordination results are obtained using the best dominant provided by the theorems and the operator previously defined as Gaussian hypergeometric function’s fractional integral. The research investigation is concluded by giving an example of how the results can be implemented.

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Section: Definition 3 ([3]mentioning

confidence: 99%

New Applications of Gaussian Hypergeometric Function for Developments on Third-Order Differential Subordinations

Oros

Preluca

2023

Symmetry

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“…A fundamental approach in the study of third-order differential superordination is to use the basic concept of admissible function as given in [10]. Using this approach, notable results were obtained by different authors examining appropriate classes of admissible functions involving generalized Bessel functions [7], fractional operators [8,11], the Srivastava-Attiya operator [12], linear operators [13,14], meromorphic functions [15] or Mittag-Leffler functions [16]. Definition 3 ([12]).…”

Section: Introductionmentioning

confidence: 99%

New Developments on the Theory of Third-Order Differential Superordination Involving Gaussian Hypergeometric Function

Oros,

Preluca

2023

Mathematics

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The present research aims to present new results regarding the fundamental problem of providing sufficient conditions for finding the best subordinant of a third-order differential superordination. A theorem revealing such conditions is first proved in a general context. As another aspect of novelty, the best subordinant is determined using the results of the first theorem for a third-order differential superordination involving the Gaussian hypergeometric function. Next, by applying the results obtained in the first proved theorem, the focus is shifted to proving the conditions for knowing the best subordinant of a particular third-order differential superordination. Such conditions are determined involving the properties of the subordination chains. This study is completed by providing means for determining the best subordinant for a particular third-order differential superordination involving convex functions. In a corollary, the conditions obtained are adapted to the special case when the convex functions involved have a more simple form.

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“…Recently, in other studies, [48][49][50][51][52][53][54]60 the authors obtained differential subordination results for multivalent functions within a generalized fractional calculus. The main idea of the technique we use here involves investigating the geometric properties of functions in [p] employing a novel convolution operator.…”

Section: Introductionmentioning

confidence: 99%

Third‐order differential subordinations for multivalent functions in the theory of source‐sink dynamics

Morais

Zayed

Srivastava

2021

Math Methods in App Sciences

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We propose third‐order differential subordination results associated with new admissible classes of multivalent functions defined in the open unit disk on the complex plane. Besides, we investigate the geometric properties of multivalent functions associated with a novel convolution operator. This is done by taking suitable linear combinations of the classical Gaussian hypergeometric function and its derivatives up to third‐order and applying the Hadamard product (or convolution) formula for power series. The complex velocity potential and the stream function of two‐dimensional potential flow problems over a circular cylinder using both sources with sink and two sources are treated by the methods developed in the present paper. We further determine the fluid flow produced by a single source and construct a univalent function so that the image of source/sink is also source/sink for a given complex potential. Finally, some plot simulations are provided to illustrate the different results of this work.

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Applications of differential subordinations involving a generalized fractional differintegral operator

Abstract: Using the third-order differential subordination basic results, we introduce certain classes of admissible functions and investigate some applications of third-order differential subordination for p-valent functions associated with generalized fractional differintegral operator.

Cited by 8 publications

References 21 publications

New Applications of Gaussian Hypergeometric Function for Developments on Third-Order Differential Subordinations

New Applications of Gaussian Hypergeometric Function for Developments on Third-Order Differential Subordinations

New Developments on the Theory of Third-Order Differential Superordination Involving Gaussian Hypergeometric Function

Third‐order differential subordinations for multivalent functions in the theory of source‐sink dynamics

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