Recent Trends on Applied Mathematics And Modeling

This thematic series hosts selective papers presented in ICAAA2012-Istanbul. This issue is focused on recent trends and new ideas in the area of Applied Mathematics and Modeling.

Edited by: Mustafa Bayram and Selcuk Kutluay

Dynamical behaviors of a discrete SIS epidemic model with standard incidence and stage structure

A discrete SIS epidemic model with stage structure and standard incident rate which is governed by Beverton-Holt type is studied. The sufficient conditions on the permanence and extinction of disease are estab...

Authors: Zhidong Teng, Linfei Nie and Jiabo Xu

Citation: Advances in Difference Equations 2013 2013:87

Content type: Research Published on: 3 April 2013
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Dark soliton and periodic wave solutions of nonlinear evolution equations

This paper studies the Kudryashov-Sinelshchikov and Jimbo-Miwa equations. Subsequently, we formally derive the dark (topological) soliton solutions for these equations. By using the sine-cosine method, some ad...

Authors: Özkan Güner, Ahmet Bekir and Adem Cengiz Cevikel

Citation: Advances in Difference Equations 2013 2013:68

Content type: Research Published on: 21 March 2013
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A switching rule for exponential stability of switched recurrent neural networks with interval time-varying delay

This paper studies the problem for exponential stability of switched recurrent neural networks with interval time-varying delay. The time delay is a continuous function belonging to a given interval, but not n...

Authors: Manlika Rajchakit, Piyapong Niamsup and Grienggrai Rajchakit

Citation: Advances in Difference Equations 2013 2013:44

Content type: Research Published on: 28 February 2013
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Dual identities in fractional difference calculus within Riemann

We investigate two types of dual identities for Riemann fractional sums and differences. The first type relates nabla- and delta-type fractional sums and differences. The second type represented by the Q-operator...

Authors: Thabet Abdeljawad

Citation: Advances in Difference Equations 2013 2013:36

Content type: Research Published on: 15 February 2013
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Dynamics of a stochastic non-autonomous predator-prey system with Beddington-DeAngelis functional response

A stochastic non-autonomous predator-prey system with Beddington-DeAngelis functional response is proposed, the existence of a global positive solution and stochastically ultimate boundedness are derived. Suff...

Authors: Shuang Li and Xinan Zhang

Citation: Advances in Difference Equations 2013 2013:19

Content type: Research Published on: 22 January 2013
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The numerical solution of partial differential-algebraic equations

In this paper, a numerical solution of partial differential-algebraic equations (PDAEs) is considered by multivariate Padé approximations. We applied this method to an example. First, PDAE has been converted t...

Authors: Muhammed Yigider and Ercan Çelik

Citation: Advances in Difference Equations 2013 2013:8

Content type: Research Published on: 10 January 2013
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Application of Hilbert transform to fault detection in electric machines

In this study we investigate the possibility of broken bar fault detection in an induction machine rotor using spectral analysis of the stator currents. The numerical method, presented in this work, based on t...

Authors: A Medoued, A Lebaroud and D Sayad

Citation: Advances in Difference Equations 2013 2013:2

Content type: Research Published on: 7 January 2013
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On the generalized Hartley-Hilbert and Fourier-Hilbert transforms

In this paper, we discuss Hartley-Hilbert and Fourier-Hilbert transforms on a certain class of generalized functions. The extended transforms considered in this article are shown to be well-defined, one-to-one...

Authors: SKQ Al-Omari and A Kılıçman

Citation: Advances in Difference Equations 2012 2012:232

Content type: Research Published on: 28 December 2012
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Lie symmetry analysis of the time-variable coefficient B-BBM equation

We perform Lie group classification of a time-variable coefficient combined Burgers and Benjamin-Bona-Mahony equations (B-BBM equation). The direct analysis of the determining equations is employed to specify ...

Authors: Motlatsi Molati and Chaudry Masood Khalique

Citation: Advances in Difference Equations 2012 2012:212

Content type: Research Published on: 11 December 2012
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Unification of probability theory on time scales

The theory of time scales was introduced by Stefan Hilger in his PhD thesis in 1988 in order to unify continuous and discrete analysis. Probability is a discipline in which appears to be many applications of t...

Authors: Ünal Ufuktepe

Citation: Advances in Difference Equations 2012 2012:211

Content type: Research Published on: 10 December 2012
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Approximate analytic solution of fractional heat-like and wave-like equations with variable coefficients using the differential transforms method

This paper uses the differential transform method (DTM) to obtain analytical solutions of fractional heat- and wave-like equations with variable coefficients. The time fractional heat-like and wave-like equati...

Authors: Aydin Secer

Citation: Advances in Difference Equations 2012 2012:198

Content type: Research Published on: 14 November 2012
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Curvature-driven diffusion-based mathematical image registration models

This paper introduces several mathematical image registration models. Image registration, an ill-posed optimization problem, is formulated as the minimization of the sum of an image similarity metric and a reg...

Authors: Mehmet Ali Akinlar, Muhammet Kurulay, Aydin Secer and Mehmet Celenk

Citation: Advances in Difference Equations 2012 2012:193

Content type: Research Published on: 7 November 2012
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A fractional order nonlinear dynamical model of interpersonal relationships

In this paper, a fractional order nonlinear dynamical model of interpersonal relationships has been introduced. The stability of equilibrium points is studied. Numerical simulations are also presented to verif...

Authors: N Ozalp and I Koca

Citation: Advances in Difference Equations 2012 2012:189

Content type: Research Published on: 2 November 2012
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Efficient solutions of systems of fractional PDEs by the differential transform method

In this paper we obtain approximate analytical solutions of systems of nonlinear fractional partial differential equations (FPDEs) by using the two-dimensional differential transform method (DTM). DTM is a num...

Authors: Aydin Secer, Mehmet Ali Akinlar and Adem Cevikel

Citation: Advances in Difference Equations 2012 2012:188

Content type: Research Published on: 2 November 2012
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Solving the fractional nonlinear Klein-Gordon equation by means of the homotopy analysis method

In this paper, the homotopy analysis method is applied to obtain the solution of nonlinear fractional partial differential equations. The method has been successively provided for finding approximate analytica...

Authors: Muhammet Kurulay

Citation: Advances in Difference Equations 2012 2012:187

Content type: Research Published on: 2 November 2012
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Some properties of the Mittag-Leffler functions and their relation with the Wright functions

This paper is a short description of our recent results on an important class of the so-called Mittag-Leffler functions, which became important as solutions of fractional order differential and integral equati...

Authors: Muhammet Kurulay and Mustafa Bayram

Citation: Advances in Difference Equations 2012 2012:181

Content type: Research Published on: 17 October 2012
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Approximate analytic solutions of the modified Kawahara equation with homotopy analysis method

In this paper, we applied the homotopy analysis method (HAM) to solve the modified Kawahara equation. Numerical results demonstrate that the methods provide efficient approaches to solving the modified Kawahar...

Authors: Muhammet Kurulay

Citation: Advances in Difference Equations 2012 2012:178

Content type: Research Published on: 11 October 2012
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