A New Analytical Series Solution with Convergence for Non linear Fractional Lienard’s Equations with Caputo Fractional Derivative
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초록
Lienard’s equations are important nonlinear differential equations with ap plication 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 conver gence 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.
Abstract
Lienard’s equations are important nonlinear differential equations with ap plication 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 conver gence 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.
참고문헌 (14)
- M. I. Asjad, "Novel Factional Differential Operator and its Application in Fluid Dy-namics", J. Prime Res. Math, 16, pp.67~79 (2020)
- T. M. Atanackovic, "Complex order fractional derivatives in viscoelasticity", Mech. Time-Depend. Mater, 20, pp.175~195 (2016)
- T. M. Atanackovic, "Fractional Calculus with Applications in Mechanics" (2014), ISTE
- Z. Feng, "On explicit exact solutions for the Lienard equation and its applications", Phys. Lett. A, 239, pp.50~56 (2002)
- K. A. Gepreel, "Optimal homotopy analysis method for nonlinear partial fractional differential equations", Math. Sci, 9, pp.47~55 (2015)
- A. Jajarmi, "A New Iterative Method for the Numerical Solution of High–Order Non-linear Fractional Boundary Value Problems", Front. Phys, 8, pp.160~169 (2020)
- R. M. Jena, "Residual Power Series Method for Solving Time-fractional Model of Vibration Equation of Large Membranes", J. Appl. Comput. Mech, 5, pp.603~615 (2019)
- Athassawat Kammanee, "Numerical Solutions of Fractional Differential Equations with Variable Coefficients by Taylor Basis Functions", Kyungpook Mathematical Journal, 61(2), pp.383~393 (2021), 경북대학교 자연과학대학 수학과
- A. A. Kilbas, "Theory and Application of Fractional Differential equations" (2006), Elsevier
- D. Kumar, "A modified numerical scheme and conver-gence analysis for fractional model of Lienard’s equation", J. Comput. Appl. Math, 339, pp.405~413 (2018)
- M. Z. Mohamed, "Comparison between the Laplace Decomposition Method and Adomian Decomposition in Time-Space Fractional Nonlinear Fractional Differential Equations", Appl. Math, 9, pp.448~458 (2018)
- A. Prakash, "Analytical method for space-fractional telegraph equation by homotopy perturbation transform method", Nonlinear Eng, 5, pp.123~128 (2016)
- A. Prakash, "Fractional variational iteration method for solv-ing time-fractional Newell-Whitehead-Segel equation", Nonlinear Eng, 8, pp.164~171 (2019)
- Hari Mohan Srivastava, "Fractional-Order Derivatives and Integrals: Introductory Overview and Recent Developments", Kyungpook Mathematical Journal, 60(1), pp.73~116 (2020), 경북대학교 자연과학대학 수학과[DOI]