<p>In this paper, we introduce a alteration of Stepanova’s mathematical model for tumor growth under immunological activity. We justify this modification because the tumor cells possess memory and heritable traits, and the mathematical model of tumor cells under immunity response reveals richer dynamic behaviors, such as chaos. Therefore, we first consider the Stepanova tumor model incorporating fractional order differential equations with piecewise constant arguments and then obtain a system of difference equations. The discrete model has three equilibrium points such as a tumor-free equilibrium point and two positive equilibrium points defined as benign and malignant case. In the malignant case, the positive equilibrium point is always unstable, while the other equilibrium points are locally asymptotically stable under some algebraic conditions. In addition, we show that the parameters tumor stimulated proliferation rate <i>µ</i>_<i>I</i>, rate of influx <i>κ</i>, fractional order parameter <i>α</i> and discretization parameter <i>h</i> have a crucial impact on the dynamic structure of the system. The occurrence of the Neimark-Sacker bifurcation, signifying the presence of quasi-periodic solutions, for tumor cells is established in the system as these parameters are modified. The numerically calculated bifurcation points give the threshold values for controlling the growth of tumor cell densities. Chaotic behavior is associated with structures resulting from the Neimark-Sacker bifurcation and can be analyzed with the Lyapunov exponent. Furthermore, we apply chaos control techniques like state feedback and hybrid control to mitigate chaotic behavior within the tumor-immune system. Thus, it is shown that the model successfully describes different dynamic behaviors such as uncontrolled tumor growth, tumor dormant state and tumor remission in the tumor-effector interaction.</p>