An adaptive pseudospectral method is presented for solving a class of multiterm fractional boundary value problems (FBVP) which involve Caputo-type fractional derivatives. The multiterm FBVP is first converted into a singular Volterra integrodifferential equation (SVIDE). By dividing the interval of the problem to subintervals, the unknown function is approximated using a piecewise interpolation polynomial with unknown coefficients which is based on shifted Legendre-Gauss (ShLG) collocation points. Then the problem is reduced to a system of algebraic equations, thus greatly simplifying the problem. Further, some additional conditions are considered to maintain the continuity of the approximate solution and its derivatives at the interface of subintervals. In order to convert the singular integrals of SVIDE into nonsingular ones, integration by parts is utilized. In the method developed in this paper, the accuracy can be improved either by increasing the number of subintervals or by increasing the degree of the polynomial on each subinterval. Using several examples including Bagley-Torvik equation the proposed method is shown to be efficient and accurate.

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caputotype fractional singular volterra integrodifferential equation multiterm fbvp singular integrals of svide interface of subintervals nonsingular unknown shifted legendregauss shlg collocation solution algebraic equations multiterm fractional boundary value problems continuity piecewise interpolation polynomial adaptive pseudospectral method bagleytorvik equation

Mohammad Maleki,Ishak Hashim,Majid Tavassoli Kajani,Saeid Abbasbandy,.An Adaptive Pseudospectral Method for Fractional Order Boundary Value Problems. 2012 (),.

Mohammad Maleki,Ishak Hashim,Majid Tavassoli Kajani,Saeid Abbasbandy,"An Adaptive Pseudospectral Method for Fractional Order Boundary Value Problems" 2012

Mohammad Maleki,Ishak Hashim,Majid Tavassoli Kajani,Saeid Abbasbandy,"An Adaptive Pseudospectral Method for Fractional Order Boundary Value Problems"