Mathematics / Matematik

Permanent URI for this collectionhttps://hdl.handle.net/11147/8

Browse

Filters

2015 - 20162

Settings

Publisher: search.filters.publisher.John Wiley and Sons Inc.Subject: search.filters.subject.Difference equations

Search Results

Now showing 1 - 2 of 2
  • Article
    Citation - WoS: 22
    Citation - Scopus: 26
    Exact Solutions for Fractional Ddes Via Auxiliary Equation Method Coupled With the Fractional Complex Transform
    (John Wiley and Sons Inc., 2016) Aslan, İsmail; Aslan, İsmail; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of Technology
    Dynamical behavior of many nonlinear systems can be described by fractional-order equations. This study is devoted to fractional differential–difference equations of rational type. Our focus is on the construction of exact solutions by means of the (G'/G)-expansion method coupled with the so-called fractional complex transform. The solution procedure is elucidated through two generalized time-fractional differential–difference equations of rational type. As a result, three types of discrete solutions emerged: hyperbolic, trigonometric, and rational. Copyright © 2016 John Wiley & Sons, Ltd. Copyright © 2016 John Wiley & Sons, Ltd.
  • Article
    Citation - WoS: 21
    Citation - Scopus: 21
    An Analytic Approach To a Class of Fractional Differential-Difference Equations of Rational Type Via Symbolic Computation
    (John Wiley and Sons Inc., 2015) Aslan, İsmail; Aslan, İsmail; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of Technology
    Fractional derivatives are powerful tools in solving the problems of science and engineering. In this paper, an analytical algorithm for solving fractional differential-difference equations in the sense of Jumarie's modified Riemann-Liouville derivative has been described and demonstrated. The algorithm has been tested against time-fractional differentialdifference equations of rational type via symbolic computation. Three examples are given to elucidate the solution procedure. Our analyses lead to closed form exact solutions in terms of hyperbolic, trigonometric, and rational functions, which might be subject to some adequate physical interpretations in the future. Copyright © 2013 JohnWiley & Sons, Ltd.