Mohammad Reza Doostdar - Department of Mathematics, Zarandieh Branch, Islamic Azad University, Zarandieh, Iran
Manochehr Kazemi - Department of Mathematics, Ashtian Branch, Islamic Azad University, Ashtian, Iran

In this paper, we present a collocation numerical technique for solving Caputo-fractionalsmoking model. Our computational scheme is based on the combination of block pulse func-tions and Legendre polynomials. The advantage of using hybrid functions is that by adjusting aproper order for the block pulse functions and the considered polynomials, an appropriate solu-tion can be achieved. In the presented scheme, by using the collocation points for the obtainedresidual, the fractional order smoking model is reduced into the system of algebraic equations.To show the efficiency and the applicability of the presented method, a numerical example issimulated. Also, the effect of the order of fractional derivative on the numerical results is studied.

Fractional calculus, Caputo fractional derivative, Smoking model, Hybrid func-tions, Collocation methods.