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On the Wavelet Collocation Method for Solving Fractional Fredholm Integro-Differential Equations

Author

Listed:
  • Haifa Bin Jebreen

    (Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia
    These authors contributed equally to this work.)

  • Ioannis Dassios

    (AMPSAS, University College Dublin, D04 V1W8 Dublin, Ireland
    These authors contributed equally to this work.)

Abstract

An efficient algorithm is proposed to find an approximate solution via the wavelet collocation method for the fractional Fredholm integro-differential equations (FFIDEs). To do this, we reduce the desired equation to an equivalent linear or nonlinear weakly singular Volterra–Fredholm integral equation. In order to solve this integral equation, after a brief introduction of Müntz–Legendre wavelets, and representing the fractional integral operator as a matrix, we apply the wavelet collocation method to obtain a system of nonlinear or linear algebraic equations. An a posteriori error estimate for the method is investigated. The numerical results confirm our theoretical analysis, and comparing the method with existing ones demonstrates its ability and accuracy.

Suggested Citation

  • Haifa Bin Jebreen & Ioannis Dassios, 2022. "On the Wavelet Collocation Method for Solving Fractional Fredholm Integro-Differential Equations," Mathematics, MDPI, vol. 10(8), pages 1-12, April.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:8:p:1272-:d:791711
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    References listed on IDEAS

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    1. Haifa Bin Jebreen & Fairouz Tchier & à tila Madureira Bueno, 2021. "A New Scheme for Solving Multiorder Fractional Differential Equations Based on Müntz–Legendre Wavelets," Complexity, Hindawi, vol. 2021, pages 1-9, July.
    2. Arikoglu, Aytac & Ozkol, Ibrahim, 2009. "Solution of fractional integro-differential equations by using fractional differential transform method," Chaos, Solitons & Fractals, Elsevier, vol. 40(2), pages 521-529.
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    Cited by:

    1. Marzban, Hamid Reza & Nezami, Atiyeh, 2022. "Analysis of nonlinear fractional optimal control systems described by delay Volterra–Fredholm integral equations via a new spectral collocation method," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).

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