Abstract
A new approximate formula of the fractional derivatives is derived. Theproposed formula is based on the generalized Laguerre polynomials. Global approximationsto functions defined on a semi-infinite interval are constructed. The fractional derivativesare presented in terms of Caputo sense. Special attention is given to study the convergenceanalysis and estimate an error upper bound of the presented formula. The new spectral Laguerrecollocation method is presented for solving fractional Logistic differential equation (FLDE). Theproperties of Laguerre polynomials approximation are used to reduce FLDE to solve a systemof algebraic equations which is solved using a suitable numerical method. Numerical results areprovided to confirm the theoretical results and the efficiency of the proposed method.