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Using operational matrix of two-dimensional Bernstein polynomials for solving two-dimensional integral equations of fractional order

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  • Asgari, M.
  • Ezzati, R.

Abstract

In this paper, we first preset two-dimensional Bernstein polynomials operational matrix (2DBPOM) for two-dimensional fractional integral equations (2DFIE). Then, we introduce a computational method based on 2DBPOM to reduce the 2DFIE to those of solving a system of algebraic equations. Also, we give the error analysis. Finally, this method is applied for solving three examples to illustrate the applicability and accuracy of presented method.

Suggested Citation

  • Asgari, M. & Ezzati, R., 2017. "Using operational matrix of two-dimensional Bernstein polynomials for solving two-dimensional integral equations of fractional order," Applied Mathematics and Computation, Elsevier, vol. 307(C), pages 290-298.
    • Handle: RePEc:eee:apmaco:v:307:y:2017:i:c:p:290-298
    DOI: 10.1016/j.amc.2017.03.012
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    References listed on IDEAS

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    1. Guo, Tian Liang & Zhang, KanJian, 2015. "Impulsive fractional partial differential equations," Applied Mathematics and Computation, Elsevier, vol. 257(C), pages 581-590.
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    Cited by:

    1. Kumar, Sunil & Kumar, Ranbir & Cattani, Carlo & Samet, Bessem, 2020. "Chaotic behaviour of fractional predator-prey dynamical system," Chaos, Solitons & Fractals, Elsevier, vol. 135(C).
    2. Ahmad Sami Bataineh & Osman Rasit Isik & Moa’ath Oqielat & Ishak Hashim, 2021. "An Enhanced Adaptive Bernstein Collocation Method for Solving Systems of ODEs," Mathematics, MDPI, vol. 9(4), pages 1-15, February.
    3. Ahmad Sami Bataineh & Osman Rasit Isik & Abedel-Karrem Alomari & Mohammad Shatnawi & Ishak Hashim, 2020. "An Efficient Scheme for Time-Dependent Emden-Fowler Type Equations Based on Two-Dimensional Bernstein Polynomials," Mathematics, MDPI, vol. 8(9), pages 1-17, September.
    4. Maleknejad, Khosrow & Rashidinia, Jalil & Eftekhari, Tahereh, 2018. "Numerical solution of three-dimensional Volterra–Fredholm integral equations of the first and second kinds based on Bernstein’s approximation," Applied Mathematics and Computation, Elsevier, vol. 339(C), pages 272-285.
    5. Sunil Kumar & Ali Ahmadian & Ranbir Kumar & Devendra Kumar & Jagdev Singh & Dumitru Baleanu & Mehdi Salimi, 2020. "An Efficient Numerical Method for Fractional SIR Epidemic Model of Infectious Disease by Using Bernstein Wavelets," Mathematics, MDPI, vol. 8(4), pages 1-22, April.
    6. Pan, Yubin & Huang, Jin & Ma, Yanying, 2019. "Bernstein series solutions of multidimensional linear and nonlinear Volterra integral equations with fractional order weakly singular kernels," Applied Mathematics and Computation, Elsevier, vol. 347(C), pages 149-161.

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