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Quasilinearization technique for solving nonlinear Riemann-Liouville fractional-order problems

Author

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  • Su, Guangwang
  • Lu, Liang
  • Tang, Bo
  • Liu, Zhenhai

Abstract

In this work, we deal with the quasilinearization technique for a class of nonlinear Riemann-Liouville fractional-order two-point boundary value problems. Using quasilinearization technique, we construct a monotone sequence of approximate solutions which has quadratic convergence to the unique solution of the original problem, and establish the corresponding convergence estimates. Moreover, the performance of the technique is examined through a numerical example, which shows that our regularization method is available and stable.

Suggested Citation

  • Su, Guangwang & Lu, Liang & Tang, Bo & Liu, Zhenhai, 2020. "Quasilinearization technique for solving nonlinear Riemann-Liouville fractional-order problems," Applied Mathematics and Computation, Elsevier, vol. 378(C).
    • Handle: RePEc:eee:apmaco:v:378:y:2020:i:c:s0096300320301685
    DOI: 10.1016/j.amc.2020.125199
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    References listed on IDEAS

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    1. Dassios, Ioannis K. & Baleanu, Dumitru I., 2018. "Caputo and related fractional derivatives in singular systems," Applied Mathematics and Computation, Elsevier, vol. 337(C), pages 591-606.
    2. Uğurlu, Ekin & Baleanu, Dumitru & Taş, Kenan, 2018. "On square integrable solutions of a fractional differential equation," Applied Mathematics and Computation, Elsevier, vol. 337(C), pages 153-157.
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    Cited by:

    1. Peng, Xiao & Wang, Yijing & Zuo, Zhiqiang, 2022. "Co-design of state-dependent switching law and control scheme for variable-order fractional nonlinear switched systems," Applied Mathematics and Computation, Elsevier, vol. 415(C).

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