A universal predictor-corrector algorithm for numerical simulation of generalized fractional differential equations

This study introduces some remarks on generalized fractional integral and differential operators, which generalize some familiar fractional integral and derivative operators, with respect to a given function. We briefly explain how to formulate representations of generalized fractional operators. Then, mainly, we propose a predictor-corrector algorithm for the numerical simulation of initial value problems involving generalized Caputo-type fractional derivatives with respect to another function. Numerical solutions of some generalized Caputo-type fractional derivative models have been introduced to demonstrate the applicability and efficiency of the presented algorithm. The proposed algorithm is expected to be widely used and utilized in the field of simulating fractional-order models.

Automated summary

The study introduces remarks on generalized fractional integral and differential operators, and proposes a predictor-corrector algorithm for numerical simulation of initial value problems involving generalized Caputo-type fractional derivatives. The numerical solutions demonstrate the applicability and efficiency of the algorithm.