Caspian Journal of Mathematical Sciences
Volume:4 Issue: 1, Winter Spring 2015

In this paper, a technique generally known as meshless numerical scheme for solving fractional dierential equations isconsidered. We approximate the exact solution by use of Radial Basis Function(RBF) collocation method. This techniqueplays an important role to reduce a fractional dierential equation to a system of equations. The numerical results demonstrate the accuracy and ability of this method.

In this paper, we obtain a suitable mathematical model for the seismic response of dams. By using the shear beam model (SB model), we give a mathematical formulation that it is a partial differential equation and transform it to the Sturm-Liouville equation.

This paper is concerned with the existence of two non-trivial weak solutions for a p(x)-Kirchho type problem by using the mountain pass theorem of Ambrosetti and Rabinowitz and Ekeland's variational principle and the theory of the variable exponent Sobolev spaces.

This paper studies the generalized version of theZakharov-Kuznetsov Benjamin-Bona-Mahoney equation. The functionalvariable method as well as the simplest equation method areapplied to obtain solitons and singular periodic solutions to theequation. There are several constraint conditions that arenaturally revealed in order for these specialized type ofsolutions to exist. The results of this paper generalizes theprevious results that are reported in earlier publications.

Let $G$ be a non-abelian group. The non-commuting graph $Gamma_G$ of $G$ is defined as the graph whose vertex set is the non-central elements of $G$ and two vertices are joined if and only if they do not commute.In this paper we study some properties of $Gamma_G$ and introduce $n$-regular $AC$-groups. Also we then obtain a formula for Szeged index of $Gamma_G$ in terms of $n$, $|Z(G)|$ and $|G|$. Moreover, we determine eccentric connectivity index of $Gamma_G$ for every non-abelian finite group $G$ in terms of the number of conjugacy classes $k(G)$ and the size of the group $G$.

Scientists are interested in find out “how to use living resources without damaging the ecosystem at the same time?” from nineteen century because the living resources are limited. Thus, the harvested rate is used as the control parameters. Moreover, the study of harvested population dynamics is more realistic.    In the present paper, some predator-prey models in which two ecologically interacting species are harvested independently with constant or variable rates have been considered. Also, the behavior of their solutions in the global and local stability aspect have been investigated. The main aim is to present a mathematical analysis for the above model.

In this paper we study the existence of infinitely many large energy solutions for the coupled system of Schr¨odinger-Maxwell’s equations    −∆u + V (x)u + φu = Hv(x, u, v) in R 3 −∆φ = u 2 in R 3 −∆v + V (x)v + ψv = Hu(x, u, v) in R 3 −∆ψ = v 2 in R 3 , via the Fountain theorem under Cerami condition. More precisely, we consider the More general case and weaken V ∗ 1 with respect to the condition V1 in [6].

In this paper an approximate analytical solution of the fractional Zakharov-Kuznetsov equations will be obtained with the help of the reduced differential transform method (RDTM).It is in-dicated that the solutions obtained by the RDTM are reliable and present an effective method for strongly nonlinear fractional partial differential equations.

The food chain refers to a natural system by which energy is transmitted from one organism to another. In fact, a food chain consists of producers, consumers and decomposition. Presence of complex food web increase the stability of the ecosystem. Classical food chain theory arises from Lotka-Volterra model. In the present paper, the dynamics behavior of three level food chain is studied. A system of 3 nonlinear ODEs for interaction modeling of three-species food chain where intraspcies competition exists indeed is studied. The first population is the prey for the second which is prey for the third one. It is clear that it is the top of food pyramid. The techniques of linearization and first integral are employed.

Parallel computing is a topic of interest for a broad scientific community since it facilitates many time-consuming algorithms in different application domains.In this paper, we introduce a novel platform for parallel computing by using MPI and OpenMP programming languages based on set of networked PCs. UMZHPC is a free Linux-based parallel computing infrastructure that has been developed to create rapid high-performance computing clusters. It can convert heterogeneous PCs which interconnected by using a private Local Area Network(LAN) into a high-performance computing cluster. In this operating system, you can monitor your cluster and build it utilizing low-cost hardware. In addition, programs can be run in parallel by simply booting the portable UMZHPC from fronted node by using only a CD or USB-flash drive. All the requisite configurations to build a cluster and to run your programs will be carried out automatically via UMZHPC. We made the operating system publicly for research purposes.

The Sturm-Liouville boundary value problem of the multi-order fractional differential equation    D α 0+ [p(t)D β 0+ u(t)] + q(t)f(t, u(t)) = 0, t ∈ (0, 1), a limt→0 t 1−βu(t) − b limt→0 t 1−α p(t)D β 0+ u(t) = 0, c limt→1 u(t) + d limt→1 p(t)D β 0+ u(t) = 0 is studied. Results on the existence of solutions are established. The analysis relies on a weighted function space and a fixed point theorem. An example is given to illustrate the efficiency of the main theorems. Keywords: multi-order fractional differential equation, SturmLiouville boundary value problems, fixed-point theorem.

In this paper, we introduce fuzzy Banach algebra and study the properties of invertible elements and its relation with opensets. We obtain some interesting results.

In this paper ill-posed linear inverse problems that arises in many applications is considered. The instability of special kind of these problems and it's relation to the kernel, is described.For finding a stable solution to these problems we need some kind of regularization that is presented. The results have been applied for a singular equation.

In this paper, quadratic rules for obtaining approximate solution of definite integrals as well as single and double integrals using spline quasi-interpolants will be illustrated. The method is applied to a few test examples to illustrate the accuracy and the implementation of the method.