A reproducing kernel Hilbert space method for solving integro-differential equations of fractional order (Q1949559)

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.