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Solving fractional pantograph delay equations by an effective computational method

Author

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  • Hashemi, M.S.
  • Atangana, A.
  • Hajikhah, S.

Abstract

In this work, we introduce a useful and efficient calculation method for solving linear fractional pantograph delay equations (FPDEs). The proposed method is primarily dependent on the least-squares approximation technique. After embedding the problem into a minimization problem, it solves the Lagrange multiplier method. The convergence analysis is theoretically proved. Finally, some numerical examples singled out to show the usefulness and capability of the suggested approach.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:matcom:v:177:y:2020:i:c:p:295-305
    DOI: 10.1016/j.matcom.2020.04.026
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    References listed on IDEAS

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    1. Hashemi, M.S., 2018. "Invariant subspaces admitted by fractional differential equations with conformable derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 107(C), pages 161-169.
    2. Atangana, Abdon & Koca, Ilknur, 2016. "Chaos in a simple nonlinear system with Atangana–Baleanu derivatives with fractional order," Chaos, Solitons & Fractals, Elsevier, vol. 89(C), pages 447-454.
    3. Abdulnasir Isah & Chang Phang & Piau Phang, 2017. "Collocation Method Based on Genocchi Operational Matrix for Solving Generalized Fractional Pantograph Equations," International Journal of Differential Equations, Hindawi, vol. 2017, pages 1-10, June.
    4. Yin Yang & Yunqing Huang, 2013. "Spectral-Collocation Methods for Fractional Pantograph Delay-Integrodifferential Equations," Advances in Mathematical Physics, Hindawi, vol. 2013, pages 1-14, November.
    5. Abbasbandy, Saeid & Kazem, Saeed & Alhuthali, Mohammed S. & Alsulami, Hamed H., 2015. "Application of the operational matrix of fractional-order Legendre functions for solving the time-fractional convection–diffusion equation," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 31-40.
    6. Li, Dongfang & Zhang, Chengjian, 2020. "Long time numerical behaviors of fractional pantograph equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 172(C), pages 244-257.
    7. 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.
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    Cited by:

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