Geodesic
A New Operational Matrix of Fractional Integration for Shifted Jacobi Polynomials
Bulletin of the Malaysian Mathematical Society, Tome 37 (2014) no. 4 Cet article a éte moissonné depuis la source Bulletin of the Malaysian Mathematical Society website

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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.
Classification : 34A08, 65M70, 33C45 
@article{BMMS_2014_37_4_a6,
     author = {A. H. Bhrawy and M. M. Tharwat and M. A. Alghamdi},
     title = {A {New} {Operational} {Matrix} of {Fractional} {Integration} for {Shifted} {Jacobi} {Polynomials}},
     journal = {Bulletin of the Malaysian Mathematical Society},
     year = {2014},
     volume = {37},
     number = {4},
     url = {http://geodesic.mathdoc.fr/item/BMMS_2014_37_4_a6/}
}
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A. H. Bhrawy; M. M. Tharwat; M. A. Alghamdi. A New Operational Matrix of Fractional Integration for Shifted Jacobi Polynomials. Bulletin of the Malaysian Mathematical Society, Tome 37 (2014) no. 4. http://geodesic.mathdoc.fr/item/BMMS_2014_37_4_a6/