A Novel Fractional-Order RothC Model

Abstract

A new fractional q-order variation of the RothC model for the dynamics of soil organic carbon is introduced. A computational method based on the discretization of the analytic solution along with the finite-difference technique are suggested and the stability results for the latter are given. The accuracy of the scheme, in terms of the temporal step size h, is confirmed through numerical testing of a constructed analytic solution. The effectiveness of the proposed discrete method is compared with that of the classical discrete RothC model. Results from real-world experiments show that, by adjusting the fractional order q and the multiplier term ζ(t,q), a better match between simulated and actual data can be achieved compared to the traditional integer-order model.