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In this study, we have successfully found some travelling wave solutions of the variant Boussinesq system and fractional system of two-dimensional Burgers' equations of fractional order by using the -expansion method. These exact solutions contain hyperbolic, trigonometric and rational function solutions. The fractional complex transform is generally used to convert a partial fractional differential equation (FDEs) with modified Riemann-Liouville derivative into ordinary differential equation. We showed that the considered transform and method are very reliable, efficient and powerful in solving wide classes of other nonlinear fractional order equations and systems.

WOS: 000461077700004, The purpose of this study was to investigate prospective middle school mathematics teachers' perspectives about mathematical modeling tasks. Specifically, prospective teachers' views about how modeling tasks are differ from textbook problems was examined. Furthermore, what prospective teachers think about how modeling tasks would reflect classroom learning environment and whether or not they could be used in mathematics teaching were examined. A basic qualitative approach was utilized in the study. Data were gathered through open-ended questionnaires at the end of the semester from 40 prospective middle school mathematics teachers who enrolled an elective modeling course. Data were analyzed using content analysis. The findings of the study showed that prospective teachers initially did not consider modeling tasks as mathematics problems. As compared to textbook problems, prospective teachers indicated that mathematical modeling problems have many differences in terms problem structure and problem solving process. Prospective teachers stated that role of a teacher and students should be changed and formative assessment and evaluation methods should be utilized in a modeling-problem based environment. While majority of prospective teachers considered that modeling-based instruction was hard to implement because of time and classroom management, if it is accomplished it may well support many mathematical thinking skills. It is proposed that mathematical modeling problems should be integrated into formal mathematics lessons or elective courses.

Lineer olmayan olusum denklemleri (NLEE) cok sayida alanda ortaya cikan problemlerin matematiksel modelleri icin temel olusturur. Gecmis yillarda, uygulamali matematikte olusum denklemleri onemli bir yer kazanmistir. Bu calisma, lineer olmayan olusum denklemleri (NLEE) icin perturbasyon yontemi olarak bilinen cok olcekli acilim metoduyla ilgilidir. Bu raporda, (1 + 1) boyutlu besinci mertebeden lineer olmayan Caudrey-Dodd-Gibbon (CDG) denkleminin analizi icin cok olcekli acilim metodu uygulanmistir ve lineer olmayan Schrodinger (NLS) tipi denklemi elde edilmistir.

WOS: 000394270500011, In this work, we have considered the modified simple equation (MSE) method for obtaining exact solutions of nonlinear fractional-order differential equations. The space-time fractional equal width (EW) and the modified equal width (mEW) equation are considered for illustrating the effectiveness of the algorithm. It has been observed that all exact solutions obtained in this paper verify the nonlinear ordinary differential equations which was obtained from nonlinear fractional-order differential equations under the terms of wave transformation relationship. The obtained results are shown graphically., Anadolu University Scientific Research Projects [1602E048], This work was partly supported by Anadolu University Scientific Research Projects (Grant No: 1602E048).

We perform a multiple-time scales analysis and compatibility condition to the short-wave model equation. We derive Korteweg–de Vries flow equation in the bi-Hamiltonian form as an amplitude equation. Copyright © 2013 John Wiley & Sons, Ltd.

WOS: 000294300800075, We perform a multiple-time scales analysis and compatibility condition to the regularized long-wave (RLW) equation. We derive Korteweg-de Vries (KdV) flow equation in the bi-Hamiltonian form as an amplitude equation

In this report, a method of multiple scales is presented for the analysis of the (1+1)-dimensional seven order Korteweg-de Vries (KdV7) equation and we derive nonlinear Schrodinger (NLS) type equation. Also we found the exact solutions for (1+1)-dimensional KdV7 equation by using the ( G/G )-expansion method. These methods are very simple and effective for getting integrability and exact solutions of KdV type equations