Open Access. Powered by Scholars. Published by Universities.®

Special Functions Commons™

Open Access. Powered by Scholars. Published by Universities.®

Articles 1 - 5 of 5

Full-Text Articles in Special Functions

On Some Fractional Integral Operators Involving Generalized Gauss Hypergeometric Functions, N. Virchenko, O. Lisetska, S. L. Kalla Dec 2010

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, Subir, Das, R. Kumar, P. K. Gupta, Hossein Jafari Dec 2010

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.


Analytic Treatment Of Vortex States In Cylindrical Superconductors In Applied Axial Magnetic Field, Andrei Ludu, J. Van Deun, M. V, Milosevic, A. Cuyt, F. M. Peeters Aug 2010

Analytic Treatment Of Vortex States In Cylindrical Superconductors In Applied Axial Magnetic Field, Andrei Ludu, J. Van Deun, M. V, Milosevic, A. Cuyt, F. M. Peeters

Publications

We solve the linear Ginzburg–Landau GL equation in the presence of a uniform magnetic field with cylindrical symmetry and we find analytic expressions for the eigenfunctions in terms of the confluent hypergeometric functions. The discrete spectrum results from an implicit equation associated to the boundary conditions and it is resolved in analytic form using the continued fractions formalism. We study the dependence of the spectrum and the eigenfunctions on the sample size and the surface conditions for solid and hollow cylindrical superconductors. Finally, the solutions of the nonlinear GL formalism are constructed as expansions in the linear GL eigenfunction basis …


The Four-Color Theorem And Chromatic Numbers Of Graphs, Sarah E. Cates Apr 2010

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), Florentin Smarandache, Jean Dezert Jan 2010

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.