The fractional subequation method is applied to solve Cahn-Hilliard and Klein-Gordon equations of fractional order. The accuracy and efficiency of the scheme are discussed for these illustrative examples.

Hossein Jafari

Haleh Tajadodi

Nematollah Kadkhoda

Dumitru Baleanu

Fractional Subequation Method for Cahn-Hilliard and Klein-Gordon Equations

As we know, intuitionistic fuzzy sets are extensions of the standard fuzzy sets. Now, in this paper, the basic definitions and properties of intuitionistic fuzzy &#x393;-hyperideals of a &#x393;-semihyperring are introduced. A few examples are presented. In particular, some characterizations of Artinian and Noetherian &#x393;-semihyperring are given.

Bayram Ali Ersoy

Bijan Davvaz

Structure of Intuitionistic Fuzzy Sets in <svg style="vertical-align:-0.0pt" height="11.175" version="1.1" viewBox="0 0 8.7375002 11.175" width="8.7375002" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.017,-0,0,-.017,.062,11.113)"><path id="x393" d="M485 501l-30 -4q-15 64 -35 90q-12 16 -33.5 22t-68.5 6h-74q-21 0 -26.5 -5t-5.5 -26v-458q0 -62 15.5 -78t83.5 -20v-28h-270v28q58 4 72 20t14 78v399q0 61 -13.5 77t-71.5 20v28h433q0 -51 10 -149z" /></g></svg>-Semihyperrings

We present a theoretical analysis of processes of pattern formation that involves organisms distribution and their interaction of spatially distributed population with cross-diffusion in a Harrison-type predator-prey model. We analyze the global behaviour of the model by establishing a Lyapunov function. We carry out the analytical study in detail and find out the certain conditions for Turing&#x2019;s instability induced by cross-diffusion. And the numerical results reveal that, on increasing the value of the half capturing saturation constant, the sequences &#x201c;spots &#x2192; spot-stripe mixtures &#x2192; stripes &#x2192; hole-stripe mixtures &#x2192; holes&#x201d; are observed. The results show that the model dynamics exhibits complex pattern replication controlled by the cross-diffusion.

Xiaoqin Wang

Yongli Cai

Cross-Diffusion-Driven Instability in a Reaction-Diffusion Harrison Predator-Prey Model

The memristor (resistor with memory), as the fourth fundamental circuit element, is a nonvolatile nanoelectronic device and holds great promise for VLSI applications. It was suggested that the meminductor (ML, inductor with memory) circuit can be built by memristor emulators. This paper further addresses the transformation mechanism in terms of constitutive relation from the memristor to the meminductor and then designs an MR-ML mutator to achieve MR-ML transformation. We also present the mutator&#x2019;s SPICE model and analyze the simulation results.

Hui Wang

Xin Wang

Chuandong Li

Ling Chen

SPICE Mutator Model for Transforming Memristor into Meminductor

The general formulation of the second-order semi-Lagrangian methods was presented for convection-dominated diffusion problems. In view of the method of lines, this formulation is in a sufficiently general fashion as to include two-step backward difference formula and Crank-Nicolson type semi-Lagrangian schemes as particular ones. And it is easy to be extended to higher-order schemes. We show that it maintains second-order accuracy even if the involved numerical characteristic lines are first-order accurate. The relationship between semi-Lagrangian methods and the modified method of characteristic is also addressed. Finally convergence properties of the semi-Lagrangian finite difference schemes are tested.

Xiaohan Long

Chuanjun Chen

General Formulation of Second-Order Semi-Lagrangian Methods for Convection-Diffusion Problems

A novel PDE-based image denoising approach is proposed in this paper. 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With respect to standard 2D Gaussian smoothing and some nonlinear PDE-based filters, this one is more efficient to remove noise from degraded images and also to reduce “staircasing” effects and preserve the image edges.

Tudor Barbu

Variational Image Denoising Approach with Diffusion Porous Media Flow

A nonlinear generalization of the famous Camassa-Holm model is investigated. Provided that initial value <svg     style="vertical-align:-3.3907pt;width:165.1875px;" id="M1" height="17.8375" version="1.1" viewBox="0 0 165.1875 17.8375" width="165.1875"  xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg">
	
		
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</svg> in the sense of distribution, and <svg     style="vertical-align:-3.3907pt;width:151.60001px;" id="M4" height="17.8375" version="1.1" viewBox="0 0 151.60001 17.8375" width="151.60001"  xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg">
	
		
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</svg>.

Shaoyong Lai

The Global Weak Solution for a Generalized Camassa-Holm Equation

Wu and Liu (2012) presented some results for the existence and uniqueness of the periodic solutions for the hematopoiesis model. This paper gives a simple approach to find an approximate period of the model.

Ji-Huan He

Periodic Solution of the Hematopoiesis Equation

We discuss the nonexistence of nontrivial solutions for the Chern-Simons-Higgs and Chern-Simons-Schr&#xf6;dinger equations. The Derrick-Pohozaev type identities are derived to prove it.

Hyungjin Huh

Nonexistence Results of Semilinear Elliptic Equations Coupled with the Chern-Simons Gauge Field

Recently, the max-min approach was systematically studied in the review article (Ji-Huan, 2012). This paper concludes that He's max-min approach is also a very much effective method for nonlinear oscillators with discontinuous terms.

Hui-Li Zhang

Fang Xie

He's Max-Min Approach to a Nonlinear Oscillator with Discontinuous Terms

About this journal

<p><em>Abstract and Applied Analysis</em> publishes research with an emphasis on important developments in classical analysis, linear and nonlinear functional analysis, ordinary and partial differential equations, optimisation theory, and control theory.</p>


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<p>Chief Editor, Dr Wong, is an associate professor at Nanyang Technological University, Singapore. Her research interests include differential equations, difference equations, integral equations, and numerical mathematics.</p>


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Abstract and Applied Analysis - Table of contents 2013

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Abstract and Applied Analysis publishes research with an emphasis on important developments in classical analysis, linear and nonlinear functional analysis, ordinary and partial differential equations, optimisation theory, and control theory.

Abstract and Applied Analysis