Nonlinear Dynamics of a Piecewise Modified ABC Fractional-Order Leukemia Model with Symmetric Numerical Simulations

Abstract

In this study, we introduce a nonlinear leukemia dynamical system for a piecewise modified ABC fractional-order derivative and analyze it for the theoretical as well computational works and examine the crossover effect of the model. For the crossover behavior of the operators, we presume a division of the period of study [0,t2] in two subclasses as I1=[0,t1], I2=[t1,t2], for t1,t2∈R with t1t2. In I1, the classical derivative is considered for the study of the leukemia growth while in I2 we presume modified ABC fractional differential operator. As a result, the study is initiated in the piecewise modified ABC sense of derivative for the dynamical systems. The novel constructed model is then studied for the solution existence and stability as well computational results. The symmetry in dynamics for all the three classes can be graphically observed in the presented six plots.

Keywords

• piecewise modified ABC derivative
• leukemia mathematical model
• existence of solutions
• Hyers–Ulam stability
• crossover behavior