Abstract
In the manuscript fractional tumour growth and decay model is studied extensively using various dynamic analysis methods such as Lyapunov exponents, bifurcation and fixed point analysis, solution and so on. The model dynamics is observed by changing order between 0.8 and 1. Chaos has been observed in this fractional tumour growth and decay model. The model is also stabilized about its equilibrium points by chaos control technique using adaptive sliding mode control scheme. Numerical simulations are carried out to validate the theoretical results. These observations may prove fruitful and provide insight to deal with the disease.