Leukemia is an aggressive form of blood cancer that develops in the bone marrow. In this study, we consider a fractional-order four compartmental mathematical model of leukemia which includes susceptible blood cells S(t), infected blood cells I(t), cancer cells C(t), and immune blood cells W(t), and we discuss the dynamics of transmission of the disease. We employ the Laplace-Adomian decomposition methods to obtain analytical solutions and the Runge-Kutta fourth-order approach to get numerical solutions for the mathematical model of leukemia. In order to illustrate the process, the convergent of the series solution is also given, and the corresponding plots against various orders of the differentiations are plotted using specific values for the model’s parameters. We compared the solutions determined from the Laplace-Adomian decomposition methods and Runge-Kutta fourth-order. Graphical results demonstrate that the Laplace Adomian Decomposition method aligns closely with the Runge-Kutta fourth order method. For various fractional parameter values α the findings reveal that the fractional-order model offers more accuracy and stability compared to the conventional integer-order model. Some plots are presented to show the reliability and simplicity of the method. Leukemia virus is one of the many infectious diseases whose dynamics of spread can be better understood through mathematical modeling and underscores the urgent need to ensure global accessibility to this approach, with the potential to save countless lives worldwide.