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A piecewise cardinal method for a class of third-kind fractional quadratic integro-differential equations involving Caputo tempered derivative

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  • Heydari, M.H.
  • Baghban, T.
  • Bayram, M.
  • Zaky, M.A.

Abstract

In this paper, we study a family of third-kind fractional quadratic integro-differential equations including the Caputo tempered derivative, a formulation that has received limited attention in the literature. To address the analytical and computational challenges posed by these equations, a robust numerical scheme is developed using the piecewise Chebyshev cardinal functions. To provide efficient computation, we derive corresponding matrices for the classical and tempered fractional integrals. The designed algorithm transforms the original problem into a nonlinear algebraic system, enabling accurate numerical approximation of the solution. We rigorously establish the existence of a unique solution. Convergence is verified analytically and supported by comprehensive numerical experiments, which demonstrate excellent accuracy, strong agreement with theoretical predictions, and exponential convergence with respect to the polynomial degree.

Suggested Citation

  • Heydari, M.H. & Baghban, T. & Bayram, M. & Zaky, M.A., 2026. "A piecewise cardinal method for a class of third-kind fractional quadratic integro-differential equations involving Caputo tempered derivative," Chaos, Solitons & Fractals, Elsevier, vol. 202(P1).
    • Handle: RePEc:eee:chsofr:v:202:y:2026:i:p1:s0960077925014791
    DOI: 10.1016/j.chaos.2025.117466
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    References listed on IDEAS

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    1. Baleanu, Dumitru & Shekari, Parisa & Torkzadeh, Leila & Ranjbar, Hassan & Jajarmi, Amin & Nouri, Kazem, 2023. "Stability analysis and system properties of Nipah virus transmission: A fractional calculus case study," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
    2. Heydari, M.H. & Razzaghi, M., 2024. "A new wavelet method for fractional integro-differential equations with ψ-Caputo fractional derivative," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 217(C), pages 97-108.
    3. Bavi, O. & Hosseininia, M. & Hajishamsaei, M. & Heydari, M.H., 2023. "Glioblastoma multiforme growth prediction using a Proliferation-Invasion model based on nonlinear time-fractional 2D diffusion equation," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    4. Heydari, M.H. & Razzaghi, M., 2021. "Piecewise Chebyshev cardinal functions: Application for constrained fractional optimal control problems," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    5. Baghban, T. & Heydari, M.H. & Bayram, M. & Zaky, M.A., 2025. "A reliable strategy for a category of third-kind nonlinear fractional integro-differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 200(P2).
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