Numerical solution of a Riemann–Liouville fractional integro-differential bound- ary value problem with a fractional nonlocal integral boundary condition is studied based on a numerical approach which preserve the geometric structure on the Lorentz Lie group. A fictitious time τ is used to transform the dependent variable y(t) into a new one u(t, τ ) := (1 + τ ) γ y(t) in an augmented space, where 0 < γ ≤ 1 is a parameter, such that under a semi-discretization method and use of a Newton-Cotes quadrature rule the original equation is converted to a system of ODEs in the space (t, τ ) and the obtained system is solved by the Group Preserving Scheme (GPS). Some illustrative examples are given to demonstrate the accuracy and implementation of the method
