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In this paper, we construct a new fractional weighted reproducing kernel space, which is the minimum space containing the exact solution. The closed form of the reproducing kernel is obtained. Using this fractional reproducing kernel space, a class of fractional integro-differential equations with a weakly singular kernel is solved. The error estimation is given. The final numerical experiments demonstrate the correctness of the theory and the effectiveness of the method.KEYWORDS fractional integro-differential equation, fractional reproducing kernel space, weakly singular kernel 1 0 k(x, )u( )d + g(x), m − 1 < ≤ m, u (k) (0) = 0, k = 0, 1, · · · , m − 1,Math Meth Appl Sci. 2018;41:3841-3855.wileyonlinelibrary.com/journal/mma

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