A numerical algorithm for solving a four-point nonlinear fractional integro-differential equations (Q1954667)

Summary: We provide a new algorithm for a four-point nonlocal boundary value problem of nonlinear integro-differential equations of fractional order \(q \in (1, 2]\) based on reproducing kernel space method. According to our work, the analytical solution of the equations is represented in the reproducing kernel space which we construct and so the \(n\)-term approximation. At the same time, the \(n\)-term approximation is proved to converge to the analytical solution. An illustrative example is also presented, which shows that the new algorithm is efficient and accurate.