Abstract
The fractional derivative of order α, with 1 < α ≤ 2 appears in several diffusion problems used in physical and engineering applications. Therefore to obtain highly accurate approximations for this derivative is of great importance. Here, we describe and compare different numerical approximations for the fractional derivative of order 1 < α ≤ 2. These approximations arise mainly from the Grünwald–Letnikov definition and the Caputo definition and they are consistent of order one and two. In the end some numerical examples are given, to compare their performance.
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