Research

31 pages, 434 KiB

Open AccessArticle

by Simon Gluzman and Vyacheslav I. Yukalov

Axioms 2023, 12(11), 1060; https://doi.org/10.3390/axioms12111060 - 20 Nov 2023

Viewed by 1131

The method of Fractional Borel Summation is suggested in conjunction with self-similar factor approximants. The method used for extrapolating asymptotic expansions at small variables to large variables, including the variables tending to infinity, is described. The method is based on the combination of [...] Read more.

The method of Fractional Borel Summation is suggested in conjunction with self-similar factor approximants. The method used for extrapolating asymptotic expansions at small variables to large variables, including the variables tending to infinity, is described. The method is based on the combination of optimized perturbation theory, self-similar approximation theory, and Borel-type transformations. General Borel Fractional transformation of the original series is employed. The transformed series is resummed in order to adhere to the asymptotic power laws. The starting point is the formulation of dynamics in the approximations space by employing the notion of self-similarity. The flow in the approximation space is controlled, and “deep” control is incorporated into the definitions of the self-similar approximants. The class of self-similar approximations, satisfying, by design, the power law behavior, such as the use of self-similar factor approximants, is chosen for the reasons of transparency, explicitness, and convenience. A detailed comparison of different methods is performed on a rather large set of examples, employing self-similar factor approximants, self-similar iterated root approximants, as well as the approximation technique of self-similarly modified Padé–Borel approximations. Full article

(This article belongs to the Special Issue Mathematical Analysis and Applications IV)

11 pages, 293 KiB

Open AccessArticle

A Time-Fractional Differential Inequality of Sobolev Type on an Annulus

by Amal Alshabanat, Eman Almoalim, Mohamed Jleli and Bessem Samet

Axioms 2023, 12(10), 993; https://doi.org/10.3390/axioms12100993 - 20 Oct 2023

Viewed by 728

Abstract

Several phenomena from natural sciences can be described by partial differential equations of Sobolev-type. On the other hand, it was shown that in many cases, the use of fractional derivatives provides a more realistic model than the use of standard derivatives. The goal [...] Read more.

Several phenomena from natural sciences can be described by partial differential equations of Sobolev-type. On the other hand, it was shown that in many cases, the use of fractional derivatives provides a more realistic model than the use of standard derivatives. The goal of this paper is to study the nonexistence of weak solutions to a time-fractional differential inequality of Sobolev-type. Namely, we give sufficient conditions for the nonexistence or equivalently necessary conditions for the existence. Our method makes use of the nonlinear capacity method, which consists in making an appropriate choice of test functions in the weak formulation of the problem. This technique has been employed in previous papers for some classes of time-fractional differential inequalities of Sobolev-type posed on the whole space

R^{N}

. The originality of this work is that the considered problem is posed on an annulus domain, which leads to some difficulties concerning the choice of adequate test functions. Full article

(This article belongs to the Special Issue Mathematical Analysis and Applications IV)

11 pages, 278 KiB

Open AccessArticle

First-Order Differential Subordinations and Their Applications

by Ali Ebadian, Rasoul Aghalary, S. Shams, Nak Eun Cho and R. Alavi

Axioms 2023, 12(8), 743; https://doi.org/10.3390/axioms12080743 - 28 Jul 2023

Viewed by 497

Abstract

In this paper, we consider some relations related to the representations of starlike and convex functions, and obtain some sufficient conditions for starlike and convex functions by using the theory of differential subordination. Actually, we generalize a result by Suffridge for analytic functions [...] Read more.

In this paper, we consider some relations related to the representations of starlike and convex functions, and obtain some sufficient conditions for starlike and convex functions by using the theory of differential subordination. Actually, we generalize a result by Suffridge for analytic functions with missing coefficients and then we apply that generalization for obtaining the different methods to the implications of starlike or convex functions. Our results generalize and improve the previous results in the literature. Full article

(This article belongs to the Special Issue Mathematical Analysis and Applications IV)

16 pages, 361 KiB

Open AccessArticle

Existence, Uniqueness and the Multi-Stability Results for a

W

-Hilfer Fractional Differential Equation

by Safoura Rezaei Aderyani, Reza Saadati, Themistocles M. Rassias and Hari M. Srivastava

Axioms 2023, 12(7), 681; https://doi.org/10.3390/axioms12070681 - 11 Jul 2023

Cited by 3 | Viewed by 669

Abstract

In this paper, we apply the well-known aggregation mappings on Mittag-Leffler-type functions to investigating new approximation error estimates of a

W

-Hilfer fractional differential equation, by a different concept of Ulam-type stability in both bounded and unbounded domains. Full article

(This article belongs to the Special Issue Mathematical Analysis and Applications IV)

26 pages, 384 KiB

Open AccessArticle

An Efficient Class of Estimators in Stratified Random Sampling with an Application to Real Data

by Shashi Bhushan, Anoop Kumar, Showkat Ahmad Lone, Sadia Anwar and Nevine M. Gunaime

Axioms 2023, 12(6), 576; https://doi.org/10.3390/axioms12060576 - 09 Jun 2023

Cited by 3 | Viewed by 1002

Abstract

This research article addresses an efficient separate and combined class of estimators for the population mean estimation based on stratified random sampling (StRS). The first order approximated expressions of bias and mean square error of the proposed separate and combined class of estimators [...] Read more.

This research article addresses an efficient separate and combined class of estimators for the population mean estimation based on stratified random sampling (StRS). The first order approximated expressions of bias and mean square error of the proposed separate and combined class of estimators are obtained. A comparative study is conducted to determine the efficiency conditions in which the suggested class of estimators outperforms the contemporary estimators. These efficiency conditions are examined through an extensive simulation study by employing a hypothetically drawn symmetrical and asymmetrical populations. The simulation results have shown that the suggested class of estimators is more effective than the other available estimators. In addition, an application of the proposed methods is also presented by examining a real data set. Full article

(This article belongs to the Special Issue Mathematical Analysis and Applications IV)

14 pages, 331 KiB

Open AccessArticle

The Cauchy–Optimal Stability Results for Cauchy–Jensen Additive Mappings in the Fuzzy Banach Space and the Unital Fuzzy Banach Space

by Zahra Eidinejad, Reza Saadati and Hari M. Srivastava

Axioms 2023, 12(4), 405; https://doi.org/10.3390/axioms12040405 - 21 Apr 2023

Viewed by 891

Abstract

In this article, we apply a new class of fuzzy control functions to approximate a Cauchy additive mapping in fuzzy Banach space (FBS). Further, considering the unital FBS (UFBS), we will investigate the isomorphisms defined in this space. By introducing several specific functions [...] Read more.

In this article, we apply a new class of fuzzy control functions to approximate a Cauchy additive mapping in fuzzy Banach space (FBS). Further, considering the unital FBS (UFBS), we will investigate the isomorphisms defined in this space. By introducing several specific functions and choosing the optimal control function from among these functions, we evaluate the Cauchy–Optimal stability (C–O-stability) for all defined mappings. Full article

(This article belongs to the Special Issue Mathematical Analysis and Applications IV)

16 pages, 326 KiB

Open AccessArticle

Pascu-Rønning Type Meromorphic Functions Based on Sălăgean-Erdély–Kober Operator

by Sheza M. El-Deeb, Gangadharan Murugusundaramoorthy, Kaliappan Vijaya and Alhanouf Alburaikan

Axioms 2023, 12(4), 380; https://doi.org/10.3390/axioms12040380 - 16 Apr 2023

Cited by 1 | Viewed by 883

Abstract

In the present investigation, we introduce a new class of meromorphic functions defined in the punctured unit disk

Δ^{*} : = {ϑ \in C : 0 < | ϑ | < 1}

by making use of the Erdély–Kober operator [...] Read more.

In the present investigation, we introduce a new class of meromorphic functions defined in the punctured unit disk

Δ^{*} : = {ϑ \in C : 0 < | ϑ | < 1}

by making use of the Erdély–Kober operator

I_{ς, ϱ}^{τ, κ}

which unifies well-known classes of the meromorphic uniformly convex function with positive coefficients. Coefficient inequalities, growth and distortion inequalities, in addition to closure properties are acquired. We also set up a few outcomes concerning convolution and the partial sums of meromorphic functions in this new class. We additionally state some new subclasses and its characteristic houses through specializing the parameters that are new and no longer studied in association with the Erdély–Kober operator thus far. Full article

(This article belongs to the Special Issue Mathematical Analysis and Applications IV)

16 pages, 311 KiB

Open AccessArticle

New Conditions for Testing the Asymptotic and Oscillatory Behavior of Solutions of Neutral Differential Equations of the Fourth Order

by Amany Nabih, Osama Moaaz, Ghada AlNemer and Elmetwally M. Elabbasy

Axioms 2023, 12(2), 219; https://doi.org/10.3390/axioms12020219 - 20 Feb 2023

Cited by 1 | Viewed by 717

Abstract

In this work, in the noncanonical case, we find new properties for a class of positive solutions of fourth-order differential equations. These properties allow us to obtain iterative criteria that exclude positive decreasing solutions, and we then establish sufficient conditions to guarantee that [...] Read more.

In this work, in the noncanonical case, we find new properties for a class of positive solutions of fourth-order differential equations. These properties allow us to obtain iterative criteria that exclude positive decreasing solutions, and we then establish sufficient conditions to guarantee that all solutions to the examined equation oscillate. The importance of applying the results to a special case of the investigated equation is demonstrated. Full article

(This article belongs to the Special Issue Mathematical Analysis and Applications IV)

15 pages, 342 KiB

Open AccessArticle

Quadratic-Phase Hilbert Transform and the Associated Bedrosian Theorem

by Hari M. Srivastava, Firdous A. Shah, Huzaifa L. Qadri, Waseem Z. Lone and Musadiq S. Gojree

Axioms 2023, 12(2), 218; https://doi.org/10.3390/axioms12020218 - 19 Feb 2023

Cited by 1 | Viewed by 1270

Abstract

The Hilbert transform is a commonly used linear operator that separates the real and imaginary parts of an analytic signal and is employed in various fields, such as filter design, signal processing, and communication theory. However, it falls short in representing signals in [...] Read more.

The Hilbert transform is a commonly used linear operator that separates the real and imaginary parts of an analytic signal and is employed in various fields, such as filter design, signal processing, and communication theory. However, it falls short in representing signals in generalized domains. To address this limitation, we propose a novel integral transform, coined the quadratic-phase Hilbert transform. The preliminary study encompasses the formulation of all the fundamental properties of the generalized Hilbert transform. Additionally, we examine the relationship between the quadratic-phase Fourier transform and the proposed transform, and delve into the convolution theorem for the quadratic-phase Hilbert transform. The Bedrosian theorem associated with the quadratic-phase Hilbert transform is explored in detail. The validity and accuracy of the obtained results were verified through simulations. Full article

(This article belongs to the Special Issue Mathematical Analysis and Applications IV)

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