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Fractional-order clique functions to solve left-sided Bessel fractional integro-differential equations

Author

Listed:
  • Rahimkhani, P.
  • Ordokhani, Y.
  • Razzaghi, M.

Abstract

In this study, we consider a new class of nonlinear integro-differential equations with the Bessel fractional integral-derivative. For solving the considered equations, fractional-order clique functions (FCFs), and some of their properties are introduced. First, we approximate the unknown function and its derivatives/integrals in terms of the FCFs. Then, we substitute these approximations and their derivatives/integrals into the considered equation. The left-sided Bessel fractional derivative/integral (LSBFD/I) of the unknown function is approximated using the properties of the FCFs and LSBFD/I. By collocating the resulting residual function at the well-known shifted Legendre points, we derive a system of nonlinear algebraic equations. In addition, convergence analysis of the proposed approach is discussed. Finally, the presented strategy is applied to some numerical experiments to verify its applicability and accuracy.

Suggested Citation

  • Rahimkhani, P. & Ordokhani, Y. & Razzaghi, M., 2025. "Fractional-order clique functions to solve left-sided Bessel fractional integro-differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 192(C).
    • Handle: RePEc:eee:chsofr:v:192:y:2025:i:c:s0960077925000384
    DOI: 10.1016/j.chaos.2025.116025
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    References listed on IDEAS

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    1. Sabermahani, Sedigheh & Ordokhani, Yadollah & Rahimkhani, Parisa, 2023. "Application of generalized Lucas wavelet method for solving nonlinear fractal-fractional optimal control problems," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    2. Rahimkhani, Parisa & Heydari, Mohammad Hossein, 2023. "Fractional shifted Morgan–Voyce neural networks for solving fractal-fractional pantograph differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 175(P2).
    3. Ansari, Alireza & Derakhshan, Mohammad Hossein, 2024. "Time–space fractional Euler–Poisson–Darboux equation with Bessel fractional derivative in infinite and finite domains," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 218(C), pages 383-402.
    4. Maurya, Rahul Kumar & Li, Dongxia & Singh, Anant Pratap & Singh, Vineet Kumar, 2024. "Numerical algorithm for a general fractional diffusion equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 223(C), pages 405-432.
    5. Elina Shishkina & Sergey Sitnik, 2019. "A Fractional Equation with Left-Sided Fractional Bessel Derivatives of Gerasimov–Caputo Type," Mathematics, MDPI, vol. 7(12), pages 1-21, December.
    6. Ansari, Alireza & Derakhshan, Mohammad Hossein, 2023. "On spectral polar fractional Laplacian," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 206(C), pages 636-663.
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