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Abstract
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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.
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