Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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A New Analytical Series Solution with Convergence for Nonlinear Fractional Lienard's Equations with Caputo Fractional Derivative

  • Khalouta, Ali (Laboratory of Fundamental and Numerical Mathematics, Department of Mathematics, Faculty of Sciences, Ferhat Abbas Setif University 1)
  • Received : 2021.08.24
  • Accepted : 2021.12.06
  • Published : 2022.09.30
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Abstract

Lienard's equations are important nonlinear differential equations with application in many areas of applied mathematics. In the present article, a new approach known as the modified fractional Taylor series method (MFTSM) is proposed to solve the nonlinear fractional Lienard equations with Caputo fractional derivatives, and the convergence of this method is established. Numerical examples are given to verify our theoretical results and to illustrate the accuracy and effectiveness of the method. The results obtained show the reliability and efficiency of the MFTSM, suggesting that it can be used to solve other types of nonlinear fractional differential equations that arise in modeling different physical problems.

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Acknowledgement

The author would like to express his gratitude to the anonymous referees. I am very grateful for your helpful comments and careful reading, which have led to the improvement of the article.

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