Şişman, Şeyma; Merdan, Mehmet

In this study, the differential equation system with a mathematical model of parasites is examined in cases where infection does not depend on transmission and defense, but on the level of infectivity and defense of the parasite and host. When discretization is applied to the differential equation, a two-dimensional discrete system is obtained in the range of t ∈ [n, n + 1] then the stability of the Neimark-Sacker bifurcation of the positive equilibrium point of this discrete system is investigated. Finally, MAPLE and MATLAB package program are used to show the accuracy of the results obtained.

Merdan, Mehmet

In this paper, the fractional variational iteration method (FVIM) was implemented to solve timefractional generalized Hirota-Satsuma coupled-KDV equation with modified Riemann-Liouville derivative. A new application of fractional variational iteration method (FVIM) was extended to derive analytical solutions in the form of a series for these equations. It is indicated that the solutions obtained by the FVIM are reliable and effective method for strongly nonlinear couple partial equations with modified Riemann-Liouville derivative. The effects of different fractional derivative for the coupled system are investigated.