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A New Approach for Solving Nonlinear Fractional Ordinary Differential Equations

Author

Listed:
  • Hassan Kamil Jassim

    (Department of Mathematics, University of Thi-Qar, Nasiriyah 64001, Iraq)

  • Mohammed Abdulshareef Hussein

    (Scientific Research Center, Al-Ayen University, Thi-Qar 64001, Iraq
    Education Directorate of Thi-Qar, Ministry of Education, Nasiriyah 64001, Iraq
    College of Technical Engineering, National University of Science and Technology, Thi-Qar 64001, Iraq)

Abstract

Recently, researchers have been interested in studying fractional differential equations and their solutions due to the wide range of their applications in many scientific fields. In this paper, a new approach called the Hussein–Jassim (HJ) method is presented for solving nonlinear fractional ordinary differential equations. The new method is based on a power series of fractional order. The proposed approach is employed to obtain an approximate solution for the fractional differential equations. The results of this study show that the solutions obtained from solving the fractional differential equations are highly consistent with those obtained by exact solutions.

Suggested Citation

  • Hassan Kamil Jassim & Mohammed Abdulshareef Hussein, 2023. "A New Approach for Solving Nonlinear Fractional Ordinary Differential Equations," Mathematics, MDPI, vol. 11(7), pages 1-13, March.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:7:p:1565-:d:1105005
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    References listed on IDEAS

    as
    1. He, Ji-Huan & Wu, Xu-Hong, 2006. "Exp-function method for nonlinear wave equations," Chaos, Solitons & Fractals, Elsevier, vol. 30(3), pages 700-708.
    2. Hassan Kamil Jassim, 2015. "New Approaches for Solving Fokker Planck Equation on Cantor Sets within Local Fractional Operators," Journal of Mathematics, Hindawi, vol. 2015, pages 1-8, December.
    3. Singh, Jagdev & Kumar, Devendra & Baleanu, Dumitru & Rathore, Sushila, 2018. "An efficient numerical algorithm for the fractional Drinfeld–Sokolov–Wilson equation," Applied Mathematics and Computation, Elsevier, vol. 335(C), pages 12-24.
    4. Singh, Jagdev & Jassim, Hassan Kamil & Kumar, Devendra, 2020. "An efficient computational technique for local fractional Fokker Planck equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 555(C).
    5. Hossein Jafari & Hassan Kamil Jassim & Dumitru Baleanu & Yu-Ming Chu, 2021. "On The Approximate Solutions For A System Of Coupled Korteweg–De Vries Equations With Local Fractional Derivative," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 29(05), pages 1-7, August.
    6. Shun-Qin Wang & Yong-Ju Yang & Hassan Kamil Jassim, 2014. "Local Fractional Function Decomposition Method for Solving Inhomogeneous Wave Equations with Local Fractional Derivative," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-7, January.
    7. Hassan Kamil Jassim & Mohammed A. Hussein, 2022. "A Novel Formulation of the Fractional Derivative with the Order α ≥ 0 and without the Singular Kernel," Mathematics, MDPI, vol. 10(21), pages 1-18, November.
    8. Sheng-Ping Yan & Hossein Jafari & Hassan Kamil Jassim, 2014. "Local Fractional Adomian Decomposition and Function Decomposition Methods for Laplace Equation within Local Fractional Operators," Advances in Mathematical Physics, Hindawi, vol. 2014, pages 1-7, June.
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    Cited by:

    1. Jiang, Y.D. & Zhang, W. & Zhang, Y.F. & Bi, Q.S., 2024. "Bursting oscillations in coupling Mathieu-van der Pol oscillator under parametric excitation," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).
    2. Xin Song & Rui Wu, 2024. "An Efficient Numerical Method for Solving a Class of Nonlinear Fractional Differential Equations and Error Estimates," Mathematics, MDPI, vol. 12(12), pages 1-12, June.

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