A Chebyshev pseudo-spectral method for solving fractional-order integro-differential equations.

*(English)*Zbl 1216.65187The authors describe the construction of a collocation method for a class of integro-differential equations of fractional order where the fractional derivatives are interpreted in Caputo’s sense.

Reviewer’s remark: The derivation is straightforward and simple, but the description given by the authors is sometimes rather unprecise or simply wrong.

For example, the fact that four boundary conditions are given in the general description of the problem under consideration in equations (1.2) and (1.3) does not match the restriction ${\alpha}_{0}$ on the order of the differential operator stated in equations (1.1). A few numerical examples are stated, but an analysis of the properties of the method is not given.

Reviewer: Kai Diethelm (Braunschweig)

##### MSC:

65R20 | Integral equations (numerical methods) |

26A33 | Fractional derivatives and integrals (real functions) |

45J05 | Integro-ordinary differential equations |