Evaluation of Fractional-Order Pantograph Delay Differential Equation via Modified Laguerre Wavelet Method

Wavelet transforms or wavelet analysis represent a recently created mathematical tool for assistance in resolving various issues. Wavelets can also be used numerical analysis. In this study, we solve pantograph delay differential equations using the Modified Laguerre method (MLWM), an effective technique. Fractional derivatives are defined Caputo operator. The convergence of suggested strategy is carefully examined. straightforward, effective, and simple comparison with previous approaches. Specific examples provided to demonstrate current scenario’s reliability accuracy. Compared other methodologies, our results show higher accuracy level. With aid tables graphs, effectiveness proposed approach by comparing actual methods demonstrating their strong agreement. For better understanding method, pointwise solution which confirm at each point method. Additionally, employing fractional-orders compared, demonstrates that when value shifts from fractional-order integer-order, result approaches exact solution. Owing its novelty scientific significance, technique additional nonlinear fractional-order.