Efficient solutions of systems of fractional PDEs by the differential transform method

Advances in Difference Equations

Aydin Secer¹  Mehmet Ali Akinlar²  Adem Cevikel³ 

[1] Department of Mathematical Engineering, Faculty of Chemical and Metallurgical Eng., Yildiz Technical University, Istanbul, Turkey;Department of Mathematics, Faculty of Art and Sciences, Bilecik Seyh Edebali University, Bilecik, Turkey;Department of Mathematics, Faculty of Art and Sciences, Yildiz Technical University, Istanbul, Turkey

关键词: fractional differential equation;    Caputo fractional derivative;    differential transform method;   

DOI  :  10.1186/1687-1847-2012-188

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

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 numerical solution technique that is based on the Taylor series expansion which constructs an analytical solution in the form of a polynomial. The traditional higher order Taylor series method requires symbolic computation. However, DTM obtains a polynomial series solution by means of an iterative procedure. The fractional derivatives are described in the Caputo fractional derivative sense. The solutions are obtained in the form of rapidly convergent infinite series with easily computable terms. DTM is compared with some other numerical methods. Computational results reveal that DTM is a highly effective scheme for obtaining approximate analytical solutions of systems of linear and nonlinear FPDEs and offers significant advantages over other numerical methods in terms of its straightforward applicability, computational efficiency, and accuracy.

【 授权许可】

CC BY