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Accepted Papers   

  • A New Third Order Approximation for Fractional Derivatives with Applications
    H. M. Nasir and K. Nafa, Sultan Qaboos University, Oman.
    ABSTRACT

    In a recent paper (H. M. Nasir and K. Nafa, A new second order approximation for fractional derivatives with applications, SQU Science Journal, preprint), the authors have devised a general procedure to construct higher order Grunwald type approximations for fractional derivatives. A new second order approximation with shift was constructed and applied to steady state fractional problems and to space fractional diffusion problems. In this paper, we use this general procedure to construct a new third order approximation for fractional derivatives. This new approximation is applied to steady state and space fractional diffusion problems to device numerical schemes. Stability and convergence of these schemes are analysed and are supported bynumerical examples.





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