Volume 37 • Number 4 • 2014   • A New Operational Matrix of Fractional Integration for Shifted Jacobi Polynomials A. H. Bhrawy, M. M. Tharwat and M. A. Alghamdi Abstract. A new shifted Jacobi operational matrix (SJOM) of fractional integration of any order is introduced and applied together with spectral tau method for solving linear fractional differential equations (FDEs). The fractional integration is described in the Riemann-Liouville sense. The numerical approach is based on the shifted Jacobi tau method. The main characteristic behind the approach using this technique is that only a limited number of shifted Jacobi polynomials is needed to obtain a satisfactory result. Illustrative examples reveal that the present method is very effective and convenient for linear muti-term FDEs. 2010 Mathematics Subject Classification: 34A08, 65M70, 33C45 Full text: PDF