Mathematical analysis of a randomized method for fractional Carathodory type equation with time-irregular coefficients

In this work, we present a novel error analysis for fractional Caratheodory type differential equations with time irregular coefficients. It is based on the filtered probability space, with Banach spaces Lp(omega;Rd)$L<^>p(\Omega;\mathbb {R}<^>d)$ and then discretized using the randomized numerical method, which is a prototype derived from the Monte Carlo method. We derive Lp(omega;Rd)$L<^>p(\Omega;\mathbb {R}<^>d)$ error estimates where these estimates also under the low regularity that the function f is not assumed to be differentiable. The convergence order is also studied. Finally, we present numerical examples that validate the theoretical conclusions, as well as to highlight the usefulness of our technique and the accuracy of error analysis.