Article
Mathematics
Tibor K. Pogany
Summary: In this article, we establish new functional bounds and uniform bounds for the lower incomplete generalized Fox-Wright functions by using the representation formulae for the McKay I-v Bessel probability distribution's cumulative distribution function. New cumulative distribution functions are generated and expressed in terms of lower incomplete Fox-Wright functions and/or generalized hypergeometric functions. In addition, bounding inequalities are obtained for these functions.
Article
Mathematics
Mohsan Raza, Sarfraz Nawaz Malik, Qin Xin, Muhey U. Din, Luminita-Ioana Cotirla
Summary: In this article, the necessary conditions for the univalence of integral operators involving two functions are studied. The conditions for the univalence of Bessel, modified Bessel, and spherical Bessel functions are included as special cases. Moreover, sufficient conditions for integral operators involving trigonometric and hyperbolic functions are provided as an application of the results.
Article
Mathematics
Ashish Verma
Summary: This paper introduces incomplete Srivastava's triple hypergeometric matrix functions using incomplete Pochhammer matrix symbols, and derives various properties and formulas related to these functions.
QUAESTIONES MATHEMATICAE
(2021)
Article
Mathematics, Applied
Richard M. Slevinsky, Hassan Safouhi
Summary: This study improves the algorithm for computing incomplete Bessel functions by developing a recurrence relation and reducing the complexity. The results show extremely high accuracy.
NUMERICAL ALGORITHMS
(2023)
Article
Mathematics, Interdisciplinary Applications
Artion Kashuri, Yahya Almalki, Ali M. Mahnashi, Soubhagya Kumar Sahoo
Summary: This paper presents a novel approach using the left and right generalized tempered fractional integral operators to establish new Hermite-Hadamard inequalities and multiplication rules for convex functions. It also provides two useful identities involving the generalized tempered fractional integral operator for differentiable functions. The results include integral inequalities of the Hermite-Hadamard type specifically designed for convex functions, and the study covers the identification of special cases and recovery of known results through comprehensive research. Furthermore, this paper offers various applications in areas such as matrices, modified Bessel functions, and q-digamma functions.
FRACTAL AND FRACTIONAL
(2023)
Article
Physics, Multidisciplinary
M. Coskun, M. Erturk
Summary: In this study, a new set of Bessel type functions was developed by inserting different hyperbolic cosine functions into the radial part of generalized Bessel functions, to improve the performance of basis sets in Hartree-Fock-Roothaan calculations. The results showed that the new basis sets outperformed conventional approaches in terms of accuracy.
Article
Mathematics
Ashish Verma, Sarasvati Yadav
Summary: This paper introduces the incomplete second Appell hypergeometric matrix functions and their properties, enriching the theory of special matrix functions. The results presented are believed to be new.
LINEAR & MULTILINEAR ALGEBRA
(2021)
Article
Mathematics
Juan Luis Gonzalez-Santander, Fernando Sanchez Lasheras
Summary: This article calculates some infinite sums involving the digamma function and obtains interesting new results, such as parameter differentiation formulas for the beta incomplete function, reduction formulas for F-3(2) hypergeometric functions, and a definite integral not found in common literature. Additionally, the article applies these sums to calculate reduction formulas for the parameter differentiation of the Mittag-Leffler function and the Wright function.
Article
Mathematics, Applied
S. Z. H. Eweis, Z. S. Mansour
Summary: In this paper, we introduce a class of polynomials B-n,alpha((k))(x;q) generated by a function including Jackson q-Bessel functions J(alpha)((k))(x; q) (k = 1,2,3), alpha > -1. We study the main properties of these polynomials, their large n degree asymptotics, and provide their connection coefficients with the q-Laguerre polynomials and little q-Legendre polynomials.
RESULTS IN MATHEMATICS
(2022)
Article
Multidisciplinary Sciences
Giuseppe Dattoli, Emanuele Di Palma, Silvia Licciardi, Elio Sabia
Summary: The paper reviews the theory of Generalized Bessel Functions and their applications in studying electro-magnetic processes, focusing on emission of bremsstrahlung radiation by ultra-relativistic electrons and operation of Free Electron Lasers. It emphasizes the importance of Generalized Bessel Functions in analyzing spectral properties of emitted radiation by relativistic charges and their flexibility in accounting for a wide variety of phenomena.
Article
Multidisciplinary Sciences
Mohamed Abdalla, Mohamed Akel, Junesang Choi
Summary: This paper introduces a modified matrix of Riemann-Liouville fractional integrals and investigates its relationship with certain functions and polynomials. It also considers the matrix in connection with Jacobi polynomials and points out potential avenues for further research on fractional integrals.
Article
Mathematics
Robert Reynolds, Allan Stauffer
Summary: This article provides some entries and errata for the book of Gradshteyn and Ryzhik originally published by Bierens de Haan, presented in tables for easy reading and referencing.
Article
Mathematics, Applied
Mohamed Abdalla
Summary: This article focuses on the evaluation of Hankel transforms involving Bessel matrix functions in the kernel, as well as their applications in special cases. The results obtained are more general and contribute to modern integral transforms with special matrix functions.
Article
Mathematics, Applied
Durmus Albayrak, Ahmet Dernek, Nese Dernek, Faruk Ucar
Summary: The paper introduces the generalized Bessel-Maitland transform and its kernel function, obtaining new identities for special cases. Several identities for the generalized Bessel-Maitland integral transform are derived using these relations, showing some special cases are related to the Laplace transform and the Hankel transform. Additionally, examples are provided as representations of the results presented.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2021)
Article
Mathematics, Applied
Shahid Khan, Saqib Hussain, Maslina Darus
Summary: This paper investigates the geometric properties of Jackson and Hahn-Exton q-Bessel functions and normalizes them for analyticity in the open unit disk E. By introducing a new operator using normalized q-Bessel functions and the concept of convolution, a new family of subclasses of analytic functions related to the generalized conic domain is defined. The inclusion relations and integral preserving properties of these subclasses of analytic functions are studied, and the q-Bernardi integral operator is used to discuss applications of the main results.
Article
Mathematics, Applied
M. S. Bruzon, T. M. Garrido, R. de la Rosa
Summary: We study a family of generalized Zakharov-Kuznetsov modified equal width equations in (2+1)-dimensions involving an arbitrary function and three parameters. By using the Lie group theory, we classify the Lie point symmetries of these equations and obtain exact solutions. We also show that this family of equations admits local low-order multipliers and derive all local low-order conservation laws through the multiplier approach.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Dohee Jung, Changbum Chun
Summary: The paper presents a general approach to enhance the Pade iterations for computing the matrix sign function by selecting an arbitrary three-point family of methods based on weight functions. The approach leads to a multi-parameter family of iterations and allows for the discovery of new methods. Convergence and stability analysis as well as numerical experiments confirm the improved performance of the new methods.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Abhishek Yadav, Amit Setia, M. Thamban Nair
Summary: In this paper, we propose a Galerkin's residual-based numerical scheme for solving a system of Cauchy-type singular integral equations using Chebyshev polynomials. We prove the well-posedness of the system and derive a theoretical error bound and convergence order. The numerical examples validate the theoretical results.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Fernando Chacon-Gomez, M. Eugenia Cornejo, Jesus Medina, Eloisa Ramirez-Poussa
Summary: The use of decision rules allows for reliable extraction of information and inference of conclusions from relational databases, but the concepts of decision algorithms need to be extended in fuzzy environments.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Ilhame Amirali, Gabil M. Amiraliyev
Summary: This paper considers the one-dimensional initial-boundary problem for a pseudoparabolic equation with a time delay. To solve this problem numerically, a higher-order difference method is constructed and the error estimate for its solution is obtained. Based on the method of energy estimates, the fully discrete scheme is shown to be convergent of order four in space and of order two in time. The given numerical results illustrate the convergence and effectiveness of the numerical method.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Tong-tong Shang, Guo-ji Tang, Wen-sheng Jia
Summary: The goal of this paper is to investigate a class of linear complementarity problems over tensor-spaces, denoted by TLCP, which is an extension of the classical linear complementarity problem. First, two classes of structured tensors over tensor-spaces (i.e., T-R tensor and T-RO tensor) are introduced and some equivalent characterizations are discussed. Then, the lower bound and upper bound of the solutions in the sense of the infinity norm of the TLCP are obtained when the problem has a solution.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Fabio Difonzo, Pawel Przybylowicz, Yue Wu
Summary: This paper focuses on the existence, uniqueness, and approximation of solutions of delay differential equations (DDEs) with Caratheodory type right-hand side functions. It presents the construction of the randomized Euler scheme for DDEs and investigates its error. Furthermore, the paper reports the results of numerical experiments.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Priyanka Roy, Geetanjali Panda, Dong Qiu
Summary: In this article, a gradient based descent line search scheme is proposed for solving interval optimization problems under generalized Hukuhara differentiability. The innovation and importance of these concepts are presented from practical and computational perspectives. The necessary condition for existence of critical point is presented in inclusion form of interval-valued gradient. Suitable efficient descent direction is chosen based on the monotonic property of the interval-valued function and specific interval ordering. Mathematical convergence of the scheme is proved under the assumption of Inexact line search. The theoretical developments are implemented with a set of interval test problems in different dimensions. A possible application in finance is provided and solved by the proposed scheme.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Zhongqian Wang, Changqing Ye, Eric T. Chung
Summary: In this paper, the constrained energy minimizing generalized multiscale finite element method (CEM-GMsFEM) with mixed boundary conditions for elasticity equations in high contrast media is developed. The method offers advantages such as independence of target region's contrast from precision and significant impact of oversampling domain sizes on numerical accuracy. Furthermore, this is the first proof of convergence of CEM-GMsFEM with mixed boundary conditions for elasticity equations. Numerical experiments demonstrate the method's performance.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Samaneh Soradi-Zeid, Maryam Alipour
Summary: The Laguerre polynomials are a new set of basic functions used to solve a specific class of optimal control problems specified by integro-differential equations, namely IOCP. The corresponding operational matrices of derivatives are calculated to extend the solution of the problem in terms of Laguerre polynomials. By considering the basis functions and using the collocation method, the IOCP is simplified into solving a system of nonlinear algebraic equations. The proposed method has been proven to have an error bound and convergence analysis for the approximate optimal value of the performance index. Finally, examples are provided to demonstrate the validity and applicability of this technique.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Almudena P. Marquez, Maria L. Gandarias, Stephen C. Anco
Summary: A generalization of the KP equation involving higher-order dispersion is studied. The Lie point symmetries and conservation laws of the equation are obtained using Noether's theorem and the introduction of a potential. Sech-type line wave solutions are found and their features, including dark solitary waves on varying backgrounds, are discussed.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Susanne Saminger-Platz, Anna Kolesarova, Adam Seliga, Radko Mesiar, Erich Peter Klement
Summary: In this article, we study real functions defined on the unit square satisfying basic properties and explore the conditions for generating bivariate copulas using parameterized transformations and other constructions.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Lulu Tian, Nattaporn Chuenjarern, Hui Guo, Yang Yang
Summary: In this paper, a new local discontinuous Galerkin (LDG) algorithm is proposed to solve the incompressible Euler equation in two dimensions on overlapping meshes. The algorithm solves the vorticity, velocity field, and potential function on different meshes. The method employs overlapping meshes to ensure continuity of velocity along the interfaces of the primitive meshes, allowing for the application of upwind fluxes. The article introduces two sufficient conditions to maintain the maximum principle of vorticity.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Cheng Wang, Jilu Wang, Steven M. Wise, Zeyu Xia, Liwei Xu
Summary: In this paper, a temporally second-order accurate numerical scheme for the Cahn-Hilliard-Magnetohydrodynamics system of equations is proposed and analyzed. The scheme utilizes a modified Crank-Nicolson-type approximation for time discretization and a mixed finite element method for spatial discretization. The modified Crank-Nicolson approximation allows for mass conservation and energy stability analysis. Error estimates are derived for the phase field, velocity, and magnetic fields, and numerical examples are presented to validate the proposed scheme's theoretical results.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Mingyu He, Wenyuan Liao
Summary: This paper presents a numerical method for solving reaction-diffusion equations in spatially heterogeneous domains, which are commonly used to model biological applications. The method utilizes a fourth-order compact alternative directional implicit scheme based on Pade approximation-based operator splitting techniques. Stability analysis shows that the method is unconditionally stable, and numerical examples demonstrate its high efficiency and high order accuracy in both space and time.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)