GENERAL MATHEMATICS NOTES

Vol. 6, No. 1, September 2011

Contents

Title: Integrals Involving I-Function

Authors: U.K. Saha, L.K. Arora and B.K. Dutta

Abstract: In this paper, we have presented certain integrals involving product of the I-function with exponential function, Gauss's hypergeometric function and Fox's H-function. The results derived here are basic in nature and may include a number of known and new results as particular cases.

PP. 1-14

Title: Solution for Boundary Value Problem of non-integer order in L²- space

Author: Azhaar H. Sallo

Abstract: In this paper, we shall prove the existence and uniqueness of a square - integrable solution in L²-space, for the  boundary value problem of non- integer order which has the form:

^cD^α_x y(x) = f(x, y(x)), 1<α ≤2

y(a) = y_a, y(b) = y_b

Where ^cD^α is the Caputo fractional derivative and a, b are positive constants with b not equal a. The contraction mapping principle has been used in establishing our main results.

PP. 15-24

Title: Combined Effect of MHD and Radiation on Unsteady Transient Free Convection Flow between Two Long Vertical Parallel Plates with Constant Temperature and Mass Diffusion

Authors: U. S.Rajput and P. K. Sahu

Abstract: The paper studies combined effects of MHD and radiation on unsteady transient free convection flow of a viscous, incompressible, electrically conducting and radiating fluid between two long vertical parallel plates with constant temperature and mass diffusion, under the assumption that the induced magnetic field is negligible. TheLaplacetransform method has been used to find the solutions for the velocity, temperature and concentration profiles. The velocity, temperature, concentration and skin-friction are studied for different parameters like Prandtl number, Schmidt number, magnetic parameter, buoyancy ratio parameter and time.

PP. 25-39

Title: On the Solution of Fractional Kinetic Equation

Authors: B.K. Dutta, L.K. Arora and J. Borah

Abstract: In this paper, the solution of a class of fractional Kinetic equation involving generalized I-function has been discussed. Special cases involving the I-function, H-function, generalized M-series, generalized Mittag-Leffer functions are also discussed. Results obtained are related to recent investigations of possible astrophysical solutions of the solar neutrino problem.

PP. 40-48

Title: A Parametric Study on Multi-Objective Integer Quadratic Programming Problems under Uncertainty

Author: Osama E. Emam

Abstract: This paper presents a parametric study on multi-objective integer quadratic programming problem under uncertainty. The proposed procedure presents a quadratic multi-objective integer programming problem with a stochastic parameters in the right hand sides, and all constraints occurs under certain probability. We consider all random variables are normally distributed. We shall be essentially concerned with three basic notions: the set of feasible parameters; the solvability set and the stability set of the first kind (SSK1). An algorithm to clarify the developed theory as well as an illustrative example is presented.

PP. 49-60

Title: The n- Dimensional Generalized Weyl Fractional Calculus Containing to n-Dimensional $\bar{H}$-Transforms

Authors: V. B. L. Chaurasia and RaviShanker Dubey

Abstract: The object of this paper is to establish a relation between the n-dimensional   $\bar{H}$-transform involving the Weyl type n-dimensional Saigo operator of fractional integration.

PP. 61-72

Title: An Optimal Distributed Control for Age-Dependent Population Diffusion System

Authors: Jun Fu, Renzhao Chen and Xuezhang Hou

Abstract: The optimal distributed control problem for age-dependent population diffusion system governed by integral partial differential equations is investigated in this paper. As new results, the existence and uniqueness of the optimal distributed control are proposed and proved, a necessary and suffcient conditions for the control to be optimal are obtained, and the optimality system consisting of integro-partial differential equations and variational inequalities are constructed in which the optimal controls can be determined. The applications of penalty shifting method for infinite dimensional systems to approximate solutions of control problems for the population system are researched. An approximation program is structured, and the convergence of the approximating sequences in appropriate Hilbert spaces is derived. The results in this paper may significantly provide theoretical reference for the practical research of the control problem in population systems.

PP. 73-85