Theoretical and numerical aspects of the Malaria transmission model with piecewise technique

In this paper, we apply piecewise derivatives with both singular and non-singular kernels to investigate a malaria model. The singular kernel is the Caputo derivative, while the non-singular kernel is the Atangana-Baleanu operator in Caputo's sense (ABC). The existence, uniqueness, and numerical algorithm of the proposed model are presented using piecewise derivatives with both kernels. The stability is also presented for the proposed model using Ulam-Hyers stability. The numerical simulations are performed considering different fractional orders and compared the results with the real data to evaluate the efficiency of the proposed approach.