Some Contiguous Relation On K-Generalised Hypergeometric Function, 2020 IIS (deemed to be University)

#### Some Contiguous Relation On K-Generalised Hypergeometric Function, Ekta Mittal, Sunil Joshi, Sona Kumari

*Applications and Applied Mathematics: An International Journal (AAM)*

In this research work our aim is to determine some contiguous relations and some integral transform of the *k*-generalised hypergeometric functions, by using the concept of “*k*-Gamma and *k*-Beta function”. “Obviously if k approaches 1”, then the contiguous function relations become Gauss contiguous relations.

Teaching And Learning Of Fluid Mechanics, 2020 Montclair State University

#### Teaching And Learning Of Fluid Mechanics, Ashwin Vaidya

*Department of Mathematics Facuty Scholarship and Creative Works*

Fluid mechanics occupies a privileged position in the sciences; it is taught in various science departments including physics, mathematics, environmental sciences and mechanical, chemical and civil engineering, with each highlighting a different aspect or interpretation of the foundation and applications of fluids. Doll’s fluid analogy [5] for this idea is especially relevant to this issue: “Emergence of creativity from complex flow of knowledge—example of Benard convection pattern as an analogy—dissipation or dispersal of knowledge (complex knowledge) results in emergent structures, i.e., creativity which in the context of education should be thought of as a unique way to arrange information so …

Finite And Infinite Integral Formulas Involving The Family Of Incomplete H-Functions, 2020 Government Engineering College

#### Finite And Infinite Integral Formulas Involving The Family Of Incomplete H-Functions, Manish K. Bansal, Devendra Kumar, Jagdev Singh, Kottakkaran Sooppy Nisar

*Applications and Applied Mathematics: An International Journal (AAM)*

Recent research focuses on the integral representations of the various type of special functions due to their potential applicability in different disciplines. In this line, we deal with several finite and infinite integrals involving the family of incomplete H-functions. Further, we point out some known and new special cases of these integrals. Finally, we establish the integral representation of incomplete H-functions.

Generalized Hermite-Based Apostol-Euler Polynomials And Their Properties, 2020 Amity University

#### Generalized Hermite-Based Apostol-Euler Polynomials And Their Properties, Aparna Chaturvedi, Prakriti Rai, S. Ahmad Ali

*Applications and Applied Mathematics: An International Journal (AAM)*

The aim of this paper is to study certain properties of generalized Apostol-Hermite-Euler polynomials with three parameters. We have shown that there is an intimate connection between these polynomials and established their elementary properties. We also established some identities by applying the generating functions and deduce their special cases and applications.

Certain Mathieu-Type Series Pertaining To Incomplete H-Functions, 2020 Malaviya National Institute of Technology

#### Certain Mathieu-Type Series Pertaining To Incomplete H-Functions, Nidhi Jolly, Manish K. Bansal, Devendra Kumar, Jagdev Singh

*Applications and Applied Mathematics: An International Journal (AAM)*

In the present article, we derive closed integral form expressions for a family of convergent Mathieu type a-series along with its alternating variants, whose terms contain incomplete H-functions, which are a notable generalization of familiar H-function. The results established herewith are very general in nature and provide an exquisite generalization of closed integral form expressions of aforementioned series whose terms contain H-function and Fox-Wright function, respectively. Next, we present some new and interesting special cases of our main results.

Chebyshev Type Inequalities Involving The Fractional Integral Operator Containing Multi-Index Mittag-Leffler Function In The Kernel, 2020 Rajasthan Technical University

#### Chebyshev Type Inequalities Involving The Fractional Integral Operator Containing Multi-Index Mittag-Leffler Function In The Kernel, S. D. Purohit, N. Jolly, M. K. Bansal, Jagdev Singh, Devendra Kumar

*Applications and Applied Mathematics: An International Journal (AAM)*

Recently, several authors have investigated Chebyshev type inequalities for numerous fractional integral operators. Being motivated by the work done by earlier researchers and their numerous applications in probability, transform theory, numerical quadrature, statistical problems and its significance in fractional boundary value problems. We aim to evaluate Chebyshev type inequalities involving fractional integral operator containing multi-index Mittag-Leffler function in the kernel. Admissible connections of the results mentioned in this article to those associated with previously established familiar fractional integral operators have been pointed out.

Extension Of Two Parameter Gamma, Beta Functions And Its Properties, 2020 JNV University Jodhpur

#### Extension Of Two Parameter Gamma, Beta Functions And Its Properties, Kuldeep S. Gehlot, Kottakkaran S. Nisar

*Applications and Applied Mathematics: An International Journal (AAM)*

In this paper, we introduce the extension of the p-k Gamma function and the p-k Beta function. This extension of the p-k Gamma function is named as p-k-b Gamma function and an extension of the beta function is p-k-b Beta function. The new extension of the Gamma and Beta function has satisfied the usual properties. Also, we prove several identities of these functions.

Some Quadratic Transformations And Reduction Formulas Associated With Hypergeometric Functions, 2020 Jamia Millia Islamia (A Central University)

#### Some Quadratic Transformations And Reduction Formulas Associated With Hypergeometric Functions, M. I. Qureshi, M. Kashif Khan

*Applications and Applied Mathematics: An International Journal (AAM)*

In this paper, we construct four summation formulas for terminating Gauss’ hypergeometric series having argument “two" and with the help of our summation formulas. We establish two quadratic transformations for Gauss’ hypergeometric function in terms of finite summation of combination of two Clausen hypergeometric functions. Further, we have generalized our quadratic transformations in terms of general double series identities as well as in terms of reduction formulas for Kampé de Fériet’s double hypergeometric function. Some results of Rathie-Nagar, Kim et al. and Choi-Rathie are also obtained as special cases of our findings.

Class Of Integrals Involving Generalized Hypergeometric Function, 2020 Wollo University

#### Class Of Integrals Involving Generalized Hypergeometric Function, D. L. Suthar, Teklay Hailay, Hafte Amsalu, Jagdev Singh

*Applications and Applied Mathematics: An International Journal (AAM)*

In this paper, we establish some definite integrals involving generalized hypergeometric function, product of algebraic functions, Jacobi function, Legendre function and general class of polynomials. Certain special cases of the main results are also pointed out.

Phylogenetic Networks And Functions That Relate Them, 2020 The University of Akron

#### Phylogenetic Networks And Functions That Relate Them, Drew Scalzo

*Williams Honors College, Honors Research Projects*

Phylogenetic Networks are defined to be simple connected graphs with exactly n labeled nodes of degree one, called leaves, and where all other unlabeled nodes have a degree of at least three. These structures assist us with analyzing ancestral history, and its close relative - phylogenetic trees - garner the same visualization, but without the graph being forced to be connected. In this paper, we examine the various characteristics of Phylogenetic Networks and functions that take these networks as inputs, and convert them to more complex or simpler structures. Furthermore, we look at the nature of functions as they relate …

Symbolic Construction Of Matrix Functions In A Numerical Environment, 2020 Georgia Southern University

#### Symbolic Construction Of Matrix Functions In A Numerical Environment, Evan D. Butterworth

*Honors College Theses*

Within the field of Computational Science, the importance of programs and tools involving systems of differential equations cannot be overemphasized. Many industrial sites, such as nuclear power facilities, are unable to safely operate without these systems. This research explores and studies matrix differential equations and their applications to real computing structures. Through the use of software such as MatLab, I have constructed a toolbox, or collection, of programs that will allow any user to easily calculate a variety of matrix functions. The first tool in this collection is a program that computes the matrix exponential, famously studied and presented by …

Certain Quadruple Hypergeometric Series And Their Integral Representations, 2019 Aden University- Khormaksar

#### Certain Quadruple Hypergeometric Series And Their Integral Representations, Maged Bin-Saad, Jihad Younis

*Applications and Applied Mathematics: An International Journal (AAM)*

While investigating the Exton's list of twenty one hyper-geometric functions of four variables and the Sharma's and Parihar's list of eighty three hyper-geometric functions of four variables, we noticed existence of new hyper-geometric series of four variables. The principal object of this paper is to introduce new hyper-geometric series of four variables and present a natural further step toward the mathematical integral presentation concerning these new series of four variables. Integral representations of Euler type and Laplace type involving Appell's hyper-geometric functions and the Horn's series of two variables, Exton's and Lauricella's triple functions and Sharma and Parihar hyper-geometric functions …

A New Method To Solve Fractional Differential Equations: Inverse Fractional Shehu Transform Method, 2019 Ferhat Abbas Sétif University 1

#### A New Method To Solve Fractional Differential Equations: Inverse Fractional Shehu Transform Method, Ali Khalouta, Abdelouahab Kadem

*Applications and Applied Mathematics: An International Journal (AAM)*

In this paper, we propose a new method called the inverse fractional Shehu transform method to solve homogenous and non-homogenous linear fractional differential equations. Fractional derivatives are described in the sense of Riemann-Liouville and Caputo. Illustrative examples are given to demonstrate the validity, efficiency and applicability of the presented method. The solutions obtained by the proposed method are in complete agreement with the solutions available in the literature.

Q-Sumudu Transforms Pertaining To The Product Of Family Of Q-Polynomials And Generalized Basic Hypergeometric Functions, 2019 Sur University College

#### Q-Sumudu Transforms Pertaining To The Product Of Family Of Q-Polynomials And Generalized Basic Hypergeometric Functions, V. K. Vyas, Ali A. Al –Jarrah, S. D. Purohit

*Applications and Applied Mathematics: An International Journal (AAM)*

The prime objective of commenced article is to determine q-Sumudu transforms of a product of unified family of q-polynomials with basic (or q-) analog of Fox’s H-function and q-analog of I-functions. Specialized cases of the leading outcome are further evaluated as q-Sumudu transform of general class of q-polynomials and q-Sumudu transforms of the basic analogs of Fox’s H-function and I-functions.

Adjoint Appell-Euler And First Kind Appell-Bernoulli Polynomials, 2019 Università degli Studi Roma Tre

#### Adjoint Appell-Euler And First Kind Appell-Bernoulli Polynomials, Pierpaolo Natalini, Paolo E. Ricci

*Applications and Applied Mathematics: An International Journal (AAM)*

The adjunction property, recently introduced for Sheffer polynomial sets, is considered in the case of Appell polynomials. The particular case of adjoint Appell-Euler and Appell-Bernoulli polynomials of the first kind is analyzed.

General Nonlinear-Material Elasticity In Classical One-Dimensional Solid Mechanics, 2019 University of New Orleans

#### General Nonlinear-Material Elasticity In Classical One-Dimensional Solid Mechanics, Ronald Joseph Giardina Jr

*University of New Orleans Theses and Dissertations*

We will create a class of generalized ellipses and explore their ability to define a distance on a space and generate continuous, periodic functions. Connections between these continuous, periodic functions and the generalizations of trigonometric functions known in the literature shall be established along with connections between these generalized ellipses and some spectrahedral projections onto the plane, more specifically the well-known multifocal ellipses. The superellipse, or Lam\'{e} curve, will be a special case of the generalized ellipse. Applications of these generalized ellipses shall be explored with regards to some one-dimensional systems of classical mechanics. We will adopt the Ramberg-Osgood relation …

Summation Formulas For The Confluent Hypergeometric Function , Φ_ 2^(2r) Of Several Variables, 2019 Aden University

#### Summation Formulas For The Confluent Hypergeometric Function , Φ_ 2^(2r) Of Several Variables, Ahmed A. Atash

*Applications and Applied Mathematics: An International Journal (AAM)*

In this paper, we establish a general summation formula for the confluent hypergeometric function Φ_{2}^{(2r) }of several variables by applying the generalized Kummer’s summation theorem due to Lavoie et al. As an applications of our main result, we obtain certain new summation formulas for the confluent hypergeometric function Φ_{2}^{4} . Also some summation and transformation formulas including a results obtained recently by Choi and Rathie have been obtained as special cases.

Associated Matrix Polynomials With The Second Kind Chebyshev Matrix Polynomials, 2019 Suez Canal University

#### Associated Matrix Polynomials With The Second Kind Chebyshev Matrix Polynomials, M. S. Metwally, M. T. Mohamed, Ayman Shehata

*Applications and Applied Mathematics: An International Journal (AAM)*

This paper deals with the study of the associated Chebyshev matrix polynomials. Associated matrix polynomials with the Chebyshev matrix polynomials are defined here. Some properties of the associated Chebyshev matrix polynomials are obtained here. Further, we prove that the associated Chebyshev matrix polynomials satisfy a matrix differential equation of the second order.

Spectral Tau-Jacobi Algorithm For Space Fractional Advection-Dispersion Problem, 2019 Helwan University

#### Spectral Tau-Jacobi Algorithm For Space Fractional Advection-Dispersion Problem, Amany S. Mohamed, Mahmoud M. Mokhtar

*Applications and Applied Mathematics: An International Journal (AAM)*

In this paper, we use the shifted Jacobi polynomials to approximate the solution of the space fractional advection-dispersion. The method is based on the Jacobi operational matrices of fractional derivative and integration. A double shifted Jacobi expansion is used as an approximating polynomial. We apply this method to solve linear and nonlinear term FDEs by using initial and boundary conditions.

Algorithms To Approximate Solutions Of Poisson's Equation In Three Dimensions, 2019 University of Mary Washington

#### Algorithms To Approximate Solutions Of Poisson's Equation In Three Dimensions, Ray Dambrose

*Rose-Hulman Undergraduate Mathematics Journal*

The focus of this research was to develop numerical algorithms to approximate solutions of Poisson's equation in three dimensional rectangular prism domains. Numerical analysis of partial differential equations is vital to understanding and modeling these complex problems. Poisson's equation can be approximated with a finite difference approximation. A system of equations can be formed that gives solutions at internal points of the domain. A computer program was developed to solve this system with inputs such as boundary conditions and a nonhomogenous source function. Approximate solutions are compared with exact solutions to prove their accuracy. The program is tested with an …