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A study on the convergence conditions of generalized differential transform method
Author(s) -
Odibat Zaid M.,
Kumar Sunil,
Shawagfeh Nabil,
Alsaedi Ahmed,
Hayat Tasawar
Publication year - 2016
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3961
Subject(s) - mathematics , power series , convergence (economics) , fractional calculus , series (stratigraphy) , taylor series , mathematical analysis , differential equation , differential (mechanical device) , economics , economic growth , paleontology , aerospace engineering , engineering , biology
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.