scholarly journals Starlikeness of Normalized Bessel Functions with Symmetric Points

2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
Maryam Nazir ◽  
Syed Zakar Hussain Bukhari ◽  
Imtiaz Ahmad ◽  
Muhammad Ashfaq ◽  
Malik Ali Raza
Keyword(s):  
Differential Equation ◽  
Bessel Functions ◽  
Starlike Functions ◽  
Radius Of Starlikeness ◽  
Bessel Differential Equation ◽  
Symmetric Points

Bessel functions are related with the known Bessel differential equation. In this paper, we determine the radius of starlikeness for starlike functions with symmetric points involving Bessel functions of the first kind for some kinds of normalized conditions. Our prime tool in these investigations is the Mittag-Leffler representation of Bessel functions of the first kind.

scholarly journals Application of the Bessel function to compute the air pollutant with the stratification of the atmospheric

2015 ◽  
Vol 18 (2) ◽  
pp. 14-20
Author(s):  
Dung Anh Tran ◽  
Hang Thi Chu ◽  
Long Ta Bui
Keyword(s):  
Differential Equation ◽  
Bessel Function ◽  
Bessel Functions ◽  
Analytic Solutions ◽  
Air Pollutant ◽  
Spherical Coordinates ◽  
Advection Diffusion Equation ◽  
Advection Diffusion ◽  
Bessel Differential Equation ◽  
Separation Of Variable

The Bessel differential equation with the Bessel function of solution has been applied. Bessel functions are the canonical solutions of Bessel's differential equation. Bessel's equation arises when finding separable solutions to Laplace's equation in cylindrical or spherical coordinates. Bessel functions are important for many problems of advection–diffusion progress and wave propagation. In this paper, authors present the analytic solutions of the atmospheric advection-diffusion equation with the stratification of the boundary condition. The solution has been found by applied the separation of variable method and Bessel’s equation.

scholarly journals On nabla discrete fractional calculus operator for a modified Bessel equation

2018 ◽  
Vol 22 (Suppl. 1) ◽  
pp. 203-209 ◽  
Author(s):  
Resat Yilmazer ◽  
Okkes Ozturk
Keyword(s):  
Differential Equation ◽  
Fractional Calculus ◽  
Bessel Functions ◽  
Discrete Fractional Calculus ◽  
Bessel Beams ◽  
Bessel Equation ◽  
Bessel Differential Equation ◽  
Thermal Sciences

In thermal sciences, it is possible to encounter topics such as Bessel beams, Bessel functions or Bessel equations. In this work, we also present new discrete fractional solutions of the modified Bessel differential equation by means of the nabla-discrete fractional calculus operator. We consider homogeneous and non-homogeneous modified Bessel differential equation. So, we acquire four new solutions of these equations in the discrete fractional forms via a newly developed method

On a singular eigenvalue problem

1968 ◽  
Vol 64 (2) ◽  
pp. 439-446 ◽  
Author(s):  
D. Naylor ◽  
S. C. R. Dennis
Keyword(s):  
Differential Equation ◽  
Eigenvalue Problem ◽  
Bessel Functions ◽  
Asymptotic Condition ◽  
Real Constant ◽  
Limit Circle ◽  
Expansion In Eigenfunctions ◽  
Image Position

Sears and Titchmarsh (1) have formulated an expansion in eigenfunctions which requires a knowledge of the s-zeros of the equationHere ka > 0 is supposed given and β is a real constant such that 0 ≤ β < π. The above equation is encountered when one seeks the eigenfunctions of the differential equationon the interval 0 < α ≤ r < ∞ subject to the condition of vanishing at r = α. Solutions of (2) are the Bessel functions J±is(kr) and every solution w of (2) is such that r−½w(r) belongs to L2 (α, ∞). Since the problem is of the limit circle type at infinity it is necessary to prescribe a suitable asymptotic condition there to make the eigenfunctions determinate. In the present instance this condition is

scholarly journals Third Hankel determinant and Zalcman functional for a class of starlike functions with respect to symmetric points related with sine function

2021 ◽  
Vol 25 (01) ◽  
pp. 29-36
Author(s):  
Muhammad Ghaffar Khan ◽  
Bakhtiar Ahmad ◽  
Gangadharan Murugusundaramoorthy ◽  
Wali Khan Mashwani ◽  
Sibel Yalçin ◽  
...  
Keyword(s):  
Starlike Functions ◽  
Sine Function ◽  
Hankel Determinant ◽  
Symmetric Points

scholarly journals Calculating Galois groups of third-order linear differential equations with parameters

2018 ◽  
Vol 20 (04) ◽  
pp. 1750038
Author(s):  
Andrei Minchenko ◽  
Alexey Ovchinnikov
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Galois Group ◽  
Galois Groups ◽  
Linear Differential Equations ◽  
Unipotent Radical ◽  
Third Order ◽  
Differential Galois Group ◽  
Bessel Differential Equation ◽  
Linear Differential

Motivated by developing algorithms that decide hypertranscendence of solutions of extensions of the Bessel differential equation, algorithms computing the unipotent radical of a parameterized differential Galois group have been recently developed. Extensions of Bessel’s equation, such as the Lommel equation, can be viewed as homogeneous parameterized linear differential equations of the third order. In this paper, we give the first known algorithm that calculates the differential Galois group of a third-order parameterized linear differential equation.

Solution to the Bessel differential equation with interactive fuzzy boundary conditions

2021 ◽  
Vol 41 (1) ◽  
Author(s):  
Daniel Eduardo Sánchez ◽  
Vinícius Francisco Wasques ◽  
Estevão Esmi ◽  
Laécio Carvalho de Barros
Keyword(s):  
Differential Equation ◽  
Boundary Conditions ◽  
Bessel Differential Equation ◽  
Fuzzy Boundary

Some properties of the analytic functions with bounded radius rotation

2019 ◽  
Vol 28 (1) ◽  
pp. 85-90
Author(s):  
YASAR POLATOGLU ◽  
◽  
ASENA CETINKAYA ◽  
OYA MERT ◽  
◽  
...  
Keyword(s):  
Analytic Functions ◽  
Unit Disc ◽  
Starlike Functions ◽  
Open Unit ◽  
Coefficient Estimate ◽  
Open Unit Disc ◽  
Radius Of Starlikeness ◽  
Growth Theorem ◽  
Bounded Radius Rotation

In the present paper, we introduce a new subclass of normalized analytic starlike functions by using bounded radius rotation associated with q- analogues in the open unit disc \mathbb D. We investigate growth theorem, radius of starlikeness and coefficient estimate for the new subclass of starlike functions by using bounded radius rotation associated with q- analogues denoted by \mathcal{R}_k(q), where k\geq2, q\in(0,1).

scholarly journals Harmonic Starlike Functions with Respect to Symmetric Points

Axioms ◽  
2019 ◽  
Vol 9 (1) ◽  
pp. 3 ◽  
Author(s):  
Nak Eun Cho ◽  
Jacek Dziok
Keyword(s):  
Integral Representation ◽  
Starlike Functions ◽  
Coefficient Estimates ◽  
Distortion Theorems ◽  
Harmonic Starlike ◽  
Symmetric Points

In the paper we define classes of harmonic starlike functions with respect to symmetric points and obtain some analytic conditions for these classes of functions. Some results connected to subordination properties, coefficient estimates, integral representation, and distortion theorems are also obtained.

Sign in / Sign up

Export Citation Format

Share Document