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An Effective Method for Solving Fractional Integrodifferential Equations of the Volterra and Fredholm Types Based on the Lucas Polynomials

Author

Listed:
  • Shabaz Jalil Mohammedfaeq
  • Miran Bayan Mohammed Amin
  • Dashne Chapuk Zahir
  • Shazad Shawki Ahmed

Abstract

This article extends a spectral collocation approach based on Lucas polynomials to numerically solve the integrodifferential equations of both Volterra and Fredholm types for multi–higher fractional order in the Caputo sense under the mixed conditions. The new approach focusses on using a matrix strategy to convert the supplied equation with conditions into an algebraic linear system of equations with unknown Lucas coefficients. The coefficients of the presumed solution are determined by the solution of this system. The Lucas coefficients are used to track how the solutions behave. This method is attractive for computation, and usage examples and explanations are provided. Additionally, certain examples are provided to demonstrate the method’s accuracy, and the least‐squares error technique is employed to reduce error terms inside the designated domain. Because of this, Python is used to write most general programs.

Suggested Citation

  • Shabaz Jalil Mohammedfaeq & Miran Bayan Mohammed Amin & Dashne Chapuk Zahir & Shazad Shawki Ahmed, 2025. "An Effective Method for Solving Fractional Integrodifferential Equations of the Volterra and Fredholm Types Based on the Lucas Polynomials," Journal of Applied Mathematics, John Wiley & Sons, vol. 2025(1).
    • Handle: RePEc:wly:jnljam:v:2025:y:2025:i:1:n:6805724
    DOI: 10.1155/jama/6805724
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    References listed on IDEAS

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    1. Jianhua Hou & Beibo Qin & Changqing Yang, 2012. "Numerical Solution of Nonlinear Fredholm Integrodifferential Equations of Fractional Order by Using Hybrid Functions and the Collocation Method," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    2. Susan H. Mohammad & Abdulghafor Mohammed Al-Rozbayani & Aliaa Burqan, 2024. "Fractional Integration via Picard Method for Solving Fractional Differential-Algebraic Systems," Journal of Applied Mathematics, Hindawi, vol. 2024, pages 1-11, July.
    3. Burcu Gürbüz & Mehmet Sezer & Coşkun Güler, 2014. "Laguerre Collocation Method for Solving Fredholm Integro‐Differential Equations with Functional Arguments," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    4. Arikoglu, Aytac & Ozkol, Ibrahim, 2007. "Solution of fractional differential equations by using differential transform method," Chaos, Solitons & Fractals, Elsevier, vol. 34(5), pages 1473-1481.
    5. Burcu Gürbüz & Mehmet Sezer & Coşkun Güler, 2014. "Laguerre Collocation Method for Solving Fredholm Integro-Differential Equations with Functional Arguments," Journal of Applied Mathematics, Hindawi, vol. 2014, pages 1-12, June.
    6. Safa’ Hamdan & Naji Qatanani & Adnan Daraghmeh, 2019. "Numerical Techniques for Solving Linear Volterra Fractional Integral Equation," Journal of Applied Mathematics, John Wiley & Sons, vol. 2019(1).
    7. Jianhua Hou & Beibo Qin & Changqing Yang, 2012. "Numerical Solution of Nonlinear Fredholm Integrodifferential Equations of Fractional Order by Using Hybrid Functions and the Collocation Method," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-11, April.
    8. Safa’ Hamdan & Naji Qatanani & Adnan Daraghmeh, 2019. "Numerical Techniques for Solving Linear Volterra Fractional Integral Equation," Journal of Applied Mathematics, Hindawi, vol. 2019, pages 1-9, December.
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