| Summary: | In this article, the numerical adaptive predictor corrector (Apc-ABM) method is presented to solve generalized Caputo fractional initial value problems. The Apc-ABM method was utilized to establish approximate series solutions. The presented technique is considered to be an extension to the original Adams–Bashforth–Moulton approach. Numerical simulations and figures are presented and discussed, in order to show the efficiency of the proposed method. In the future, we anticipate that the provided generalized Caputo fractional derivative and the suggested method will be utilized to create and simulate a wide variety of generalized Caputo-type fractional models. We have included examples to demonstrate the accuracy of the present method.
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