A study on the convergence conditions of generalized differential transform method
Corresponding Author
Zaid M. Odibat
Department of Mathematics, Faculty of Science, Al-Balqa' Applied University, Salt 19117, Jordan
Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia
Correspondence to: Zaid M. Odibat, Department of Mathematics, Faculty of Science, Al-Balqa' Applied University, Salt 19117, Jordan.
E-mail: [email protected]
Search for more papers by this authorSunil Kumar
Department of Mathematics, National Institute of Technology, Jamshedpur 801014, Jharkhand, India
Search for more papers by this authorNabil Shawagfeh
Department of Mathematics, Faculty of Science, Al-Balqa' Applied University, Salt 19117, Jordan
Search for more papers by this authorAhmed Alsaedi
Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia
Search for more papers by this authorTasawar Hayat
Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia
Department of Mathematics, Quaid-I-Azam University, Islamabad 44000, Pakistan
Search for more papers by this authorCorresponding Author
Zaid M. Odibat
Department of Mathematics, Faculty of Science, Al-Balqa' Applied University, Salt 19117, Jordan
Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia
Correspondence to: Zaid M. Odibat, Department of Mathematics, Faculty of Science, Al-Balqa' Applied University, Salt 19117, Jordan.
E-mail: [email protected]
Search for more papers by this authorSunil Kumar
Department of Mathematics, National Institute of Technology, Jamshedpur 801014, Jharkhand, India
Search for more papers by this authorNabil Shawagfeh
Department of Mathematics, Faculty of Science, Al-Balqa' Applied University, Salt 19117, Jordan
Search for more papers by this authorAhmed Alsaedi
Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia
Search for more papers by this authorTasawar Hayat
Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia
Department of Mathematics, Quaid-I-Azam University, Islamabad 44000, Pakistan
Search for more papers by this authorAbstract
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.
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