In this paper, the application of the operational matrix of fractional-order Legendre functions
(FLFs) to solve the time-fractional convection–diffusion equation has been investigated.
Fractional calculus has been applied to model the engineering and physical processes which
are best described with other mathematical tools. The time variable of the time-fractional
convection–diffusion equation and its space variable have been approximated by FLFs and
shifted Legendre polynomials, respectively. The fractional derivatives together with product
matrices of FLFs are employed to convert the solution of this problem to the solution of a
system of algebraic equations
