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

Parisa Rahimkhani and Thabet Abdeljawad

Mathematics and Computers in Simulation (MATCOM), 2026, vol. 239, issue C, 790-804

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.

Keywords: χ-Riemann–Liouville fractional integral; χ-Caputo fractional derivative; Fractional-order Genocchi wavelets; Collocation method (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:239:y:2026:i:c:p:790-804

DOI: 10.1016/j.matcom.2025.07.031

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