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

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.