Journal of Hyperstructures
Volume:3 Issue: 2, Summer and Autumn 2014

The note studies further properties and results of analysis in the setting of hyper metric spaces. Among others, we present some results concerning the hyper uniform limit of a sequence of continuous functions, the hyper metric identification theorem and the metrization problem for hyper metric space.

Throughout $R$ is a Noetherian local ring. In this paper we study cohomological dimension of an $R$-module $M$ with respect to a pair of ideals and some of its relations with the attached prime ideals of $M$ and the cohomological dimension of $M$ with respect to an ideal. Furthermore, we generalize some results of \cite{DJ} in particular, Theorem 2.8.

Let M be a unitary module over a commutative ring R with identity. In this paper we consider the concepts of Artinian, semi-Artinian, reduced and multipli- cation modules. Also we call an R-module M radical, if it has no maximal submod- ule. By P(M) we denote the sum of the radical submodule of M and we show that P(M=(P(M)) = 0.

In this paper an approximate analytical solution of a mathematical modeling of reaction-diffusion Brusselator system with fractional time derivative will be obtained with the help of the reduced differential transform method. Fractional reaction-diffusion Brusselator system is used for modeling of certain chemical reaction-diffusion processes. The fractional derivatives are described in the Caputo sense. It is indicated that the solutions obtained by the reduced differential transform method are reliable and present an effective method for strongly nonlinear partial equations.

In this paper, the application of asymptotic expansion method on fractional perturbated equations are studied. Further- more, the proposed scheme is employed to obtain an analytical solution of fractional Black-Scholes equation for a European option pricing problem. Finally, the asymptotical Mittag-Leffler stability of this problem will be discussed.

In this article, a numerical method is developed to solve the linear integrodifferential equations. To this end, it will be divided in two forms, Fredholm integro-differential equations (FIDE) and Volterra integro-differential equations (VIDE). So that, the kernel and other known functions have been approximated using the least-squares approximation schemes based on Legender-Bernstein basis. The Legender polynomials are orthogonal and this property improve the accuracy of the approximations. Also the unknown function and its derivatives have been approximated by using the Bernstein basis. The useful properties of Bernstein polynomials help us to transform integro-differential equations to solve a system of linear algebraic equations. Of course, the solution way of (FIDE) case is different from (VIDE).

In this paper pricing formula for exchange option in a fractional Black-Scholes model with jumps is derived. We found out some errors in proof of pricing formula for European call option \cit {xia}. At first we revise these errors and then extend this result to pricing formula for exchange option in fractional Black-Scholes model with jumps.