Adaptation Of Residual Power Series Approach For Solving Time-Fractional Nonlinear Kline-Gordon Equations With Conformable Derivative

Authors

Rasha Amryeen, Pusat Pengajian Informatik & Matematik Gunaan, Universiti Malaysia Terengganu, 21030 Kuala Nerus, Terengganu, MalaysiaFollow
Fatimah Noor Harun, Pusat Pengajian Informatik & Matematik Gunaan, Universiti Malaysia Terengganu, 21030 Kuala Nerus, Terengganu, MalaysiaFollow
Mohammed Al-Smadi, Department of Applied Science, Ajloun College, Al-Balqa Applied University, Ajloun 26816, JordanFollow
Azwani Alias, Pusat Pengajian Informatik & Matematik Gunaan, Universiti Malaysia Terengganu, 21030 Kuala Nerus, Terengganu, MalaysiaFollow

Author Country (or Countries)

Jordan

Abstract

In this paper, the time-fractional nonlinear Kline-Gordon equations are considered and solved using the adaptive of residual power series method. The fractional derivative is considered in a conformable sense. Analytical solutions are obtained based on conformable Taylor series expansion by substituting the truncated conformable series solutions to residual error functions. This adaptation can be implemented as a novel alternative technique to handle many nonlinear issues occurring in physics and engineering. Effectiveness, validity, and feasibility of the proposed method are demonstrated by testing some numerical applications. Tabular and graphic results indicate that the method is superior, accurate and appropriate for solving these fractional partial differential models with compatible derivatives.

Digital Object Identifier (DOI)

http://dx.doi.org/10.18576/amis/140405

Recommended Citation

Amryeen, Rasha; Noor Harun, Fatimah; Al-Smadi, Mohammed; and Alias, Azwani (2020) "Adaptation Of Residual Power Series Approach For Solving Time-Fractional Nonlinear Kline-Gordon Equations With Conformable Derivative," Applied Mathematics & Information Sciences: Vol. 14: Iss. 4, Article 5.
DOI: http://dx.doi.org/10.18576/amis/140405
Available at: https://digitalcommons.aaru.edu.jo/amis/vol14/iss4/5