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Application of χ-fractional Genocchi wavelets for solving χ-fractional differential equations

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  • Rahimkhani, Parisa
  • Abdeljawad, Thabet

Abstract

This paper proposes an efficient approximation technique to solve χ-fractional differential equations, and χ-fractional delay differential equations. The method relies on utilizing a new type of functions called the χ-fractional Genocchi wavelets. The characteristics of χ-fractional Genocchi wavelets basis functions are provided and illustrated. An exact formula, employing the regularized beta function, is presented for computing the χ−Riemann–Liouville fractional integral operator of these functions. This formula, the provided wavelets, and the collocation method are employed to find the solutions of χ-fractional differential equations, and χ-fractional delay differential equations. The method’s convergence is rigorously justified. Finally, three numerical examples are presented to illustrate the efficiency and precision of this method.

Suggested Citation

  • Rahimkhani, Parisa & Abdeljawad, Thabet, 2026. "Application of χ-fractional Genocchi wavelets for solving χ-fractional differential equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 239(C), pages 790-804.
    • Handle: RePEc:eee:matcom:v:239:y:2026:i:c:p:790-804
    DOI: 10.1016/j.matcom.2025.07.031
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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. 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. Singh, Somveer & Patel, Vijay Kumar & Singh, Vineet Kumar, 2018. "Application of wavelet collocation method for hyperbolic partial differential equations via matrices," Applied Mathematics and Computation, Elsevier, vol. 320(C), pages 407-424.
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