A reproducing kernel Hilbert space method for solving integro-differential equations of fractional order. (English) Zbl 1273.65194

The authors, using the notion of the fractional derivative of Caputo, construct an approximate method to solve the integro-differential equation of fractional order of the special form \[ D^{\alpha}u(x)= F(x, u(x), Tu(x)),\qquad m-1<\alpha\leq m,\qquad 0\leq x\leq 1, \] with \( Tu(x)=\int^{x}_{0}h(x,t)u(t)dt.\) The solution \( u(x)\) is presented as convergent power series. The algorithm of the numerical computations is not strictly formulated.


65R20 Numerical methods for integral equations
26A33 Fractional derivatives and integrals
45G10 Other nonlinear integral equations
45J05 Integro-ordinary differential equations
46E22 Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces)
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