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A study on the convergence conditions of generalized differential transform method |
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| Authors: | Zaid M Odibat Sunil Kumar Nabil Shawagfeh Ahmed Alsaedi Tasawar Hayat |
| Institution: | 1. Department of Mathematics, Faculty of Science, Al‐Balqa' Applied University, Salt 19117, Jordan;2. Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia;3. Department of Mathematics, National Institute of Technology, Jamshedpur 801014, Jharkhand, India;4. Department of Mathematics, Quaid‐I‐Azam University, Islamabad 44000, Pakistan |
| Abstract: | 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 © 2016 John Wiley & Sons, Ltd. |
| Keywords: | generalized Taylor's formula generalized differential transform method Caputo fractional derivative fractional power series convergence maximum absolute truncated error |