Further Results On Fractional Calculus Of Saigo Operators, 2012 Anand International College of Engineering

#### Further Results On Fractional Calculus Of Saigo Operators, Praveen Agarwal

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

A significantly large number of earlier works on the subject of fractional calculus give interesting account of the theory and applications of fractional calculus operators in many different areas of mathematical analysis (such as ordinary and partial differential equations, integral equations, special functions, summation of series, et cetera). The main object of the present paper is to study and develop the Saigo operators. First, we establish two results that give the image of the product of multivariable H-function and a general class of polynomials in Saigo operators. On account of the general nature of the Saigo operators, multivariable H-function and …

Distributional Properties Of Record Values Of The Ratio Of Independent Exponential And Gamma Random Variables, 2012 Miami Dade College

#### Distributional Properties Of Record Values Of The Ratio Of Independent Exponential And Gamma Random Variables, M. Shakil, M. Ahsanullah

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

Both exponential and gamma distributions play pivotal roles in the study of records because of their wide applicability in the modeling and analysis of life time data in various fields of applied sciences. In this paper, a distribution of record values of the ratio of independent exponential and gamma random variables is presented. The expressions for the cumulative distribution functions, moments, hazard function and Shannon entropy have been derived. The maximum likelihood, method of moments and minimum variance linear unbiased estimators of the parameters, using record values and the expressions to calculate the best linear unbiased predictor of record values, …

Local Estimates For The Koornwinder Jacobi-Type Polynomials, 2011 University of Prishtin

#### Local Estimates For The Koornwinder Jacobi-Type Polynomials, Valmir Krasniqi, Naim L. Braha, Armend S. Shabani

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

In this paper we give some local estimates for the Koornwinder Jacobi-type polynomials by using asymptotic properties of Jacobi orthogonal polynomials.

On Some Fractional Integral Operators Involving Generalized Gauss Hypergeometric Functions, 2010 National Technical University of Ukraine “KPI

#### On Some Fractional Integral Operators Involving Generalized Gauss Hypergeometric Functions, N. Virchenko, O. Lisetska, S. L. Kalla

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

The object of this paper is to give a generalization of Gauss hypergeometric function, and to investigate its basic properties. Further, we define some fractional integral operators and their inverses in terms of the Mellin transform. Several well known integral operators, including Saigo operators can be derived from the results established here.

Approximate Analytical Solutions For Fractional Space- And Time- Partial Differential Equations Using Homotopy Analysis Method, 2010 Banaras Hindu University

#### Approximate Analytical Solutions For Fractional Space- And Time- Partial Differential Equations Using Homotopy Analysis Method, Subir, Das, R. Kumar, P. K. Gupta, Hossein Jafari

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

This article presents the approximate analytical solutions of first order linear partial differential equations (PDEs) with fractional time- and space- derivatives. With the aid of initial values, the explicit solutions of the equations are solved making use of reliable algorithm like homotopy analysis method (HAM). The speed of convergence of the method is based on a rapidly convergent series with easily computable components. The fractional derivatives are described in Caputo sense. Numerical results show that the HAM is easy to implement and accurate when applied to space- time- fractional PDEs.

The Four-Color Theorem And Chromatic Numbers Of Graphs, 2010 Lynchburg College

#### The Four-Color Theorem And Chromatic Numbers Of Graphs, Sarah E. Cates

*Undergraduate Theses and Capstone Projects*

We study graph colorings of the form made popular by the four-color theorem. Proved by Appel and Haken in 1976, the Four-Color Theorem states that all planar graphs can be vertex-colored with at most four colors. We consider an alternate way to prove the Four-Color Theorem, introduced by Hadwiger in 1943 and commonly know as Hadwiger’s Conjecture. In addition, we examine the chromatic number of graphs which are not planar. More specifically, we explore adding edges to a planar graph to create a non-planar graph which has the same chromatic number as the planar graph which we started from.

Advances And Applications Of Dsmt For Information Fusion (In Chinese), 2010 University of New Mexico

#### Advances And Applications Of Dsmt For Information Fusion (In Chinese), Florentin Smarandache, Jean Dezert

*Branch Mathematics and Statistics Faculty and Staff Publications*

No abstract provided.