MDPI - Publisher of Open Access Journals

12 pages, 325 KiB

Open AccessArticle

Coefficient Estimation Utilizing the Faber Polynomial for a Subfamily of Bi-Univalent Functions

by Abdullah Alsoboh, Ala Amourah, Fethiye Müge Sakar, Osama Ogilat, Gharib Mousa Gharib and Nasser Zomot

Axioms 2023, 12(6), 512; https://doi.org/10.3390/axioms12060512 - 24 May 2023

Cited by 8 | Viewed by 1555

Abstract

The paper introduces a new family of analytic bi-univalent functions that are injective and possess analytic inverses, by employing a q-analogue of the derivative operator. Moreover, the article establishes the upper bounds of the Taylor–Maclaurin coefficients of these functions, which can aid in approximating the accuracy of approximations using a finite number of terms. The upper bounds are obtained by approximating analytic functions using Faber polynomial expansions. These bounds apply to both the initial few coefficients and all coefficients in the series, making them general and early, respectively. Full article

(This article belongs to the Special Issue New Developments in Geometric Function Theory II)

9 pages, 289 KiB

Open AccessArticle

Estimates for the Coefficients of Subclasses Defined by the Bell Distribution of Bi-Univalent Functions Subordinate to Gegenbauer Polynomials

by Ala Amourah, Omar Alnajar, Maslina Darus, Ala Shdouh and Osama Ogilat

Mathematics 2023, 11(8), 1799; https://doi.org/10.3390/math11081799 - 10 Apr 2023

Cited by 15 | Viewed by 1569

Abstract

In the real world there are many applications that find the Bell distribution to be a useful and relevant model. One of these is the normal distribution. In this paper, we develop a new subclass of analytic bi-univalent functions by making use of the Bell distribution as a building block. These functions involve the Gegenbauer polynomials, and we use them to establish our new subclass. In this study, we solve the Fekete–Szegö functional problem and analyse various different estimates of the Maclaurin coefficients

|D_{2}|

and

|D_{3}|

for functions that belong to the built class. Full article

(This article belongs to the Special Issue Complex Analysis and Geometric Function Theory, 2nd Edition)

16 pages, 873 KiB

Open AccessArticle

Laplace-Residual Power Series Method for Solving Time-Fractional Reaction–Diffusion Model

by Moa’ath N. Oqielat, Tareq Eriqat, Osama Ogilat, Ahmad El-Ajou, Sharifah E. Alhazmi and Shrideh Al-Omari

Fractal Fract. 2023, 7(4), 309; https://doi.org/10.3390/fractalfract7040309 - 2 Apr 2023

Cited by 24 | Viewed by 2724

Abstract

Despite the fact the Laplace transform has an appreciable efficiency in solving many equations, it cannot be employed to nonlinear equations of any type. This paper presents a modern technique for employing the Laplace transform LT in solving the nonlinear time-fractional reaction–diffusion model. The new approach is called the Laplace-residual power series method (L-RPSM), which imitates the residual power series method in determining the coefficients of the series solution. The proposed method is also adapted to find an approximate series solution that converges to the exact solution of the nonlinear time-fractional reaction–diffusion equations. In addition, the method has been applied to many examples, and the findings are found to be impressive. Further, the results indicate that the L-RPSM is effective, fast, and easy to reach the exact solution of the equations. Furthermore, several actual and approximate solutions are graphically represented to demonstrate the efficiency and accuracy of the proposed method. Full article

(This article belongs to the Special Issue Recent Advances in Fractional Differential Equations and Their Applications)

► Show Figures

Figure 1

13 pages, 296 KiB

Open AccessArticle

A Generalization of Gegenbauer Polynomials and Bi-Univalent Functions

by Ala Amourah, Abdullah Alsoboh, Osama Ogilat, Gharib Mousa Gharib, Rania Saadeh and Maha Al Soudi

Axioms 2023, 12(2), 128; https://doi.org/10.3390/axioms12020128 - 28 Jan 2023

Cited by 36 | Viewed by 2686

Abstract

Three subclasses of analytic and bi-univalent functions are introduced through the use of

q -

Gegenbauer polynomials, which are a generalization of Gegenbauer polynomials. For functions falling within these subclasses, coefficient bounds

|a_{2}|

and

|a_{3}|

as well as Fekete–Szegö inequalities are [...] Read more.

Three subclasses of analytic and bi-univalent functions are introduced through the use of

q -

Gegenbauer polynomials, which are a generalization of Gegenbauer polynomials. For functions falling within these subclasses, coefficient bounds

|a_{2}|

and

|a_{3}|

as well as Fekete–Szegö inequalities are derived. Specializing the parameters used in our main results leads to a number of new results. Full article

(This article belongs to the Special Issue Recent Advances in Complex Analysis and Applications)

Search Results (4)

Further Information

Guidelines

MDPI Initiatives

Follow MDPI

Saved Queries

Search Filter Reset All

Years

Feature Papers

Subjects

Journals

Article Types

Countries / Regions

Search Results (4)

Further Information

Guidelines

MDPI Initiatives

Follow MDPI