Advances in Analysis

6

Authors: Yanqin Liu and Wen Chen

A novel modification of the variational iteration method (VIM) is proposed by means of the Sumudu transform. This approach is a universal way to identify the multiplier, which is simple and effective, and successfully extended to ordinary differential equations, including the nonlinear and variable coefficient ones. The Lagrange multiplier can be easily identified by the Sumudu transform and the nonlinear term will be handled by the Adomian series. Examples are given to elucidate the process and the reliability of the method.

7

Authors: Yaé Ulrich Gaba

In this article, we introduce a new type of contractive self maps defined in G-metric type spaces and prove a common fixed point theorem. We establish that under the convergence of a certain series, a family of self maps have a common fixed point.

12

Authors: Moustafa El-Shahed, A. M. Ahmed, Ibrahim. M. E. Abdelstar

In this paper, a fractional-order model for the spread of pests in tea plants is presented. This model consists of three components: tea plant, pest, and predator. The stability of the boundary and positive fixed points is studied. The global stability properties of the positive equilibrium point are also investigated. In addition, fractional Hopf bifurcation conditions for the model are proposed. The generalized Adams-Bashforth-Moulton method is used to solve and simulate the system of fractional differential equations.

19

Authors: Isabella Cravero, Catterina Dagnino and Sara Remogna

In this paper we consider and analyse NURBS based on bivariate quadratic B-splines on criss-cross triangulations of the parametric domain Ω0 = [0, 1] × [0, 1], presenting their main properties, showing their performances to exactly construct quadric surfaces and reporting some applications related to the modeling of objects. Moreover, we propose applications to the numerical solution of partial differential equations, with mixed boundary conditions on a given physical domain Ω, by using three different spline methods to set the prescribed Dirichlet boundary conditions.

7

Authors: K.P.R.Rao, Sk.Sadik, S.V.K.Sarma

In this paper, we obtain a unique common coupled fixed point theorem for four self maps using property(E.A.)in complex valued b-metric spaces. Also we give an example to illustrate our main theorem.

10

Authors: P Sumati Kumari, I.Ramabhadra Sarma, J.Madhusudana Rao

In this paper, we intended to explain through some examples the usefulness and necessity of studying the topological properties of weaker forms of distance spaces.

21

Authors: Chaosheng Zhu

This paper is devoted to the large time behavior and especially to the regularity of the global attractor of the dissipative 1D nonlinear Schrödinger equation with nonlocal integral term on R. We first prove that the existence of the global attractor Aγ in the strong topology of H1 (R) and the existence of the exponential attractor M which contains the global attractor Aγ, are still finite dimensional, and attract the trajectories exponentially fast. We also show that the global attractor Aγ is regular, i.e., Aγ is included, bounded and compact in H2 (R) assuming that the forcing term f(x) is of class H2 (R). Furthermore we estimate the number of the determining modes for this equation. Moreover, we show that the solution trajectories and the global attractor of the nonlocal Schrödinger equation converge to those of the usual Schrödinger equation, as the coefficient of the nonlocal integral term goes to zero.