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Description: |
In this work we are concerned with the numerical approximation of fractional di fferential equations. We will focus on initial and terminal value problems for ordinary di fferential equations of non-integer order. The approach used is based on the equivalence between this kind of problems and integral equations (Volterra and Fredholm integral equations, respectively). Taking into account the potential non-smoothness of the solution of such problems, we propose a collocation method which uses a non-polynomial approximation on a uniform mesh. A convergence analysis is provided and some numerical results are presented and discussed.
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