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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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