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    Numerical solution of some fractional partial differential equations using collocation finite element method
    (Natural Sciences Publishing, 2015) Ucar, Yusuf; Yagmurlu, Nuri Murat; Tasbozan, Orkun; Esen, Alaattin
    In this work, our aim is to obtain a numerical solution to some fractional differential equations. In the solution process, we have used fractional derivatives in Caputo sense. The fundamental characteristics of the present method is the fact that it converts complex problems into those requiring the solution of algebraic ones, which is obviously more easy for computational processing. The obtained approximate values show the accuracy and suitability of the present scheme for applying a wide range of fractional partial differential equations. Finally, the error norms L2 and L? are computed and found to be sufficiently small. © 2015 NSP.
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    Öğe
    Numerical Solution of Time Fractional Burgers Equation by Cubic B-spline Finite Elements
    (Springer Basel Ag, 2016) Esen, Alaattin; Tasbozan, Orkun
    We present some numerical examples which support numerical results for the time fractional Burgers equation with various boundary and initial conditions obtained by collocation method using cubic B-spline base functions. The aim of this paper is to show that the finite element method based on the cubic B-spline collocation method approach is also suitable for the treatment of the fractional differential equations. The results of numerical experiments are compared with analytical solution to confirm the accuracy and efficiency of the presented scheme.