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Numerical solution of nonlinear delay differential equations of fractional order in reproducing kernel Hilbert space

Author

Listed:
  • Ghasemi, M.
  • Fardi, M.
  • Khoshsiar Ghaziani, R.

Abstract

In this paper, approximate solutions to a class of fractional differential equations with delay are presented by using a semi-analytical approach in Hilbert function space. Further, the uniqueness of the solution is proved in the space of real-valued continuous functions, as well as the existence of the solution is proved in Hilbert function space. We also prove convergence and perform an analysis error for the proposed approach. Sophisticated delay differential equations of fractional order are considered as test examples. Numerical results illustrate the efficiency of the proposed approach computationally.

Suggested Citation

  • Ghasemi, M. & Fardi, M. & Khoshsiar Ghaziani, R., 2015. "Numerical solution of nonlinear delay differential equations of fractional order in reproducing kernel Hilbert space," Applied Mathematics and Computation, Elsevier, vol. 268(C), pages 815-831.
    • Handle: RePEc:eee:apmaco:v:268:y:2015:i:c:p:815-831
    DOI: 10.1016/j.amc.2015.06.012
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    Citations

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    Cited by:

    1. Li, Xiuying & Li, Haixia & Wu, Boying, 2019. "Piecewise reproducing kernel method for linear impulsive delay differential equations with piecewise constant arguments," Applied Mathematics and Computation, Elsevier, vol. 349(C), pages 304-313.
    2. Chen, Zhong & Gou, QianQian, 2019. "Piecewise Picard iteration method for solving nonlinear fractional differential equation with proportional delays," Applied Mathematics and Computation, Elsevier, vol. 348(C), pages 465-478.
    3. Du, Mingjing & Qiao, Xiaohua & Wang, Biao & Wang, Yulan & Gao, Bo, 2019. "A novel method for numerical simulation of sand motion model in beach formation based on fractional Taylor–Jumarie series expansion and piecewise interpolation technique," Applied Mathematics and Computation, Elsevier, vol. 347(C), pages 15-21.
    4. Hashemi, M.S. & Atangana, A. & Hajikhah, S., 2020. "Solving fractional pantograph delay equations by an effective computational method," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 177(C), pages 295-305.
    5. Zeid, Samaneh Soradi, 2019. "Approximation methods for solving fractional equations," Chaos, Solitons & Fractals, Elsevier, vol. 125(C), pages 171-193.

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