Bhrawy, A. H.E. H., DohaBaleanu, DEzz-Eldien, S. S.2019-11-062019-11-062015https://doi.org/10.1016/j.jcp.2014.03.039https://www.sciencedirect.com/science/article/pii/S0021999114002265In this paper, an efficient and accurate spectral numerical method is presented for solving second-, fourth-order fractional diffusion-wave equations and fractional wave equations with damping. The proposed method is based on Jacobi tau spectral procedure together with the Jacobi operational matrix for fractional integrals, described in the Riemann-Liouville sense. The main characteristic behind this approach is to reduce such problems to those of solving systems of algebraic equations in the unknown expansion coefficients of the sought-for spectral approximations. The validity and effectiveness of the method are demonstrated by solving five numerical examples. Numerical examples are presented in the form of tables and graphs to make comparisons with the results obtained by other methods and with the exact solutions more easier. (C) 2014 Elsevier Inc. All rights reserved.enOctober University for University for Fractional diffusion-wave equationsTau methodShifted Jacobi polynomials; Operational matrixCaputo derivativeArticlehttps://doi.org/10.1016/j.jcp.2014.03.039