A study on the convergence conditions of generalized differential transform method

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• 作者：Zaid M. Odibat ; Sunil Kumar ; Nabil Shawagfeh ; Ahmed Alsaedi and Tasawar Hayat
• 刊名：Mathematical Methods in the Applied Sciences
• 出版年：2017
• 出版时间：15 January 2017
• 年：2017
• 卷：40
• 期：1
• 页码：40-48
• 全文大小：563K
• ISSN：1099-1476

文摘

This paper deals with constructing generalized ‘fractional’ power series representation for solutions of fractional order differential equations. We present a brief review of generalized Taylor's series and generalized differential transform methods. Then, we study the convergence of fractional power series. Our emphasis is to address the sufficient condition for convergence and to estimate the truncated error. Numerical simulations are performed to estimate maximum absolute truncated error when the generalized differential transform method is used to solve non-linear differential equations of fractional order. The study highlights the power of the generalized differential transform method as a tool in obtaining fractional power series solutions for differential equations of fractional order. Copyright