Some numerical schemes for the caputo fractional derivative

In this study, we compare three numerical schemes, namely Adam-Bashforth-Moulton (FAM), a fractional Adams method of predictor-corrector order 2 (FAM22), and a fractional explicit Adams method order 3 (FEAM3). Those schemes are applied to solve the fractional initial value problem (FIVP) that deals with four test functions in the Caputo operator. All of the FIVPs have analytical solutions. To gauge how accurate the numerical schemes are, we use root mean square error (RMSE). We varied the order of fractional derivatives between 0 and 1 and the step size of the scheme. The experiment findings show that size of the step and order alpha have an impact on how accurate the approximation solution provided by each method is. The accuracy approximation and order of accuracy grow as a increases and tends to 1. In contrast, the accuracy increases as the step size grows.