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Operator-based approach for the construction of analytical soliton solutions to nonlinear fractional-order differential equations

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  • Navickas, Z.
  • Telksnys, T.
  • Marcinkevicius, R.
  • Ragulskis, M.

Abstract

An operator-based framework for the construction of analytical soliton solutions to fractional differential equations is presented in this paper. Fractional differential equations are mapped from Caputo algebra to Riemann-Liouville algebra in order to preserve the additivity of base function powers under multiplication. The proposed technique is used for the construction of solutions to a class of fractional Riccati equations. Recurrence relations between power series parameters yield generating functions which are used to construct explicit expressions of closed-form solutions.

Suggested Citation

  • Navickas, Z. & Telksnys, T. & Marcinkevicius, R. & Ragulskis, M., 2017. "Operator-based approach for the construction of analytical soliton solutions to nonlinear fractional-order differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 625-634.
    • Handle: RePEc:eee:chsofr:v:104:y:2017:i:c:p:625-634
    DOI: 10.1016/j.chaos.2017.09.026
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    References listed on IDEAS

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    1. Cang, Jie & Tan, Yue & Xu, Hang & Liao, Shi-Jun, 2009. "Series solutions of non-linear Riccati differential equations with fractional order," Chaos, Solitons & Fractals, Elsevier, vol. 40(1), pages 1-9.
    2. Pakdaman, M. & Ahmadian, A. & Effati, S. & Salahshour, S. & Baleanu, D., 2017. "Solving differential equations of fractional order using an optimization technique based on training artificial neural network," Applied Mathematics and Computation, Elsevier, vol. 293(C), pages 81-95.
    3. Kudryashov, Nikolai A., 2005. "Simplest equation method to look for exact solutions of nonlinear differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 24(5), pages 1217-1231.
    4. Kashkari, Bothayna S.H. & Syam, Muhammed I., 2016. "Fractional-order Legendre operational matrix of fractional integration for solving the Riccati equation with fractional order," Applied Mathematics and Computation, Elsevier, vol. 290(C), pages 281-291.
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    Cited by:

    1. Inga Timofejeva & Zenonas Navickas & Tadas Telksnys & Romas Marcinkevicius & Minvydas Ragulskis, 2021. "An Operator-Based Scheme for the Numerical Integration of FDEs," Mathematics, MDPI, vol. 9(12), pages 1-17, June.

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