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Adomian Decomposition and Fractional Power Series Solution of a Class of Nonlinear Fractional Differential Equations

Author

Listed:
  • Pshtiwan Othman Mohammed

    (Department of Mathematics, College of Education, University of Sulaimani, Sulaimani 46001, Kurdistan Region, Iraq)

  • José António Tenreiro Machado

    (Institute of Engineering, Polytechnic of Porto, Department of Electrical Engineering, Rua Dr. António Bernardino de Almeida, 431, 4249-015 Porto, Portugal)

  • Juan L. G. Guirao

    (Department of Applied Mathematics and Statistics, Technical University of Cartagena, Hospital de Marina, 30203 Cartagena, Spain
    Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia)

  • Ravi P. Agarwal

    (Department of Mathematics, Texas A & M University-Kingsville, Kingsville, TX 78363, USA)

Abstract

Nonlinear fractional differential equations reflect the true nature of physical and biological models with non-locality and memory effects. This paper considers nonlinear fractional differential equations with unknown analytical solutions. The Adomian decomposition and the fractional power series methods are adopted to approximate the solutions. The two approaches are illustrated and compared by means of four numerical examples.

Suggested Citation

  • Pshtiwan Othman Mohammed & José António Tenreiro Machado & Juan L. G. Guirao & Ravi P. Agarwal, 2021. "Adomian Decomposition and Fractional Power Series Solution of a Class of Nonlinear Fractional Differential Equations," Mathematics, MDPI, vol. 9(9), pages 1-18, May.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:9:p:1070-:d:551480
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    References listed on IDEAS

    as
    1. Pshtiwan Othman Mohammed & Thabet Abdeljawad & Fahd Jarad & Yu-Ming Chu, 2020. "Existence and Uniqueness of Uncertain Fractional Backward Difference Equations of Riemann–Liouville Type," Mathematical Problems in Engineering, Hindawi, vol. 2020, pages 1-8, October.
    2. Manar A. Alqudah & Pshtiwan Othman Mohammed & Thabet Abdeljawad, 2020. "Solution of Singular Integral Equations via Riemann–Liouville Fractional Integrals," Mathematical Problems in Engineering, Hindawi, vol. 2020, pages 1-8, September.
    3. Changyou Wang & Haiqiang Zhang & Shu Wang, 2012. "Positive Solution of a Nonlinear Fractional Differential Equation Involving Caputo Derivative," Discrete Dynamics in Nature and Society, Hindawi, vol. 2012, pages 1-16, October.
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    Cited by:

    1. Kamsing Nonlaopon & Awais Gul Khan & Farah Ameen & Muhammad Uzair Awan & Clemente Cesarano, 2022. "Multi-Step Quantum Numerical Techniques for Finding the Solutions of Nonlinear Equations," Mathematics, MDPI, vol. 10(15), pages 1-17, July.
    2. Sabermahani, Sedigheh & Ordokhani, Yadollah & Rahimkhani, Parisa, 2023. "Application of generalized Lucas wavelet method for solving nonlinear fractal-fractional optimal control problems," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    3. Xiaoming Wang & Shehbaz Ahmad Javed & Abdul Majeed & Mohsin Kamran & Muhammad Abbas, 2022. "Investigation of Exact Solutions of Nonlinear Evolution Equations Using Unified Method," Mathematics, MDPI, vol. 10(16), pages 1-17, August.
    4. Leonard Dăuş & Ghiocel Groza & Marilena Jianu, 2022. "Full Hermite Interpolation and Approximation in Topological Fields," Mathematics, MDPI, vol. 10(11), pages 1-17, May.

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