Comparison of dynamical behavior between fractional order delayed and discrete conformable fractional order tumor-immune system

In this paper, we analyze the dynamical behavior of delayed fractional-order tumor model with Caputo sense and discretized conformable model. The is constituted group nonlinear differential equations having effector cells. First all, stability bifurcation analysis in fractional derivative studied, existence Hopf depending on time delay parameter proved by using center manifold theory. Applying discretization process based piecewise constant arguments to version gives a two-dimensional discrete system. Stability Neimark–Sacker system are demonstrated Schur-Cohn criterion projection method. This study reveals that τ h discrete-time have similar effects corresponding systems. Moreover, effect order systems discussed. Finally, all results obtained interpreted biologically, numerical simulations presented illustrate support theoretical results.