Optimal Control and Spectral Collocation Method for Solving Smoking Models

In this manuscript, we solve the ordinary model of nonlinear smoking mathematically by using second kind shifted Chebyshev polynomials. The stability equilibrium point is calculated. schematic illustrates our proposition. We discuss optimal control model, and formularize work through necessary optimality cases. A numerical technique for simulation problem adopted. Moreover, a method presented, its analysis discussed. Numerical then demonstrates idea. Optimal further discussed clarifying drawing before after control. Fractional request differential equations (FDEs) are usually used to display frameworks that have memory exist in few thermoelasticity models organic standards. FDEs show realistic biphasic decline infection diseases but at slower rate. more suitable than integer order ones modeling complex systems, such as biological systems.