Fast Evaluation of the Caputo Fractional Derivative and Its Applications to Fractional Diffusion Equations
نویسندگان
چکیده
Abstract. We present an efficient algorithm for the evaluation of the Caputo fractional derivative C0D α t f(t) of order α ∈ (0, 1), which can be expressed as a convolution of f (t) with the kernel t. The algorithm is based on an efficient sum-of-exponentials approximation for the kernel t on the interval [∆t, T ] with a uniform absolute error ε, where the number of exponentials Nexp needed is of the order O (
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تاریخ انتشار 2015