  In this work, we present a collocation method based on the Legendre wavelet
combined with the Gauss--Jacobi quadrature formula for solving a class of
fractional delay-type integro-differential equations. The problem is considered
with either initial or boundary conditions and the fractional derivative is
described in the Caputo sense. First, an approximation of the unknown solution
is considered in terms of the Legendre wavelet basis functions. Then, we
substitute this approximation and its derivatives into the considered equation.
The Caputo derivative of the unknown function is approximated using the
Gauss--Jacobi quadrature formula. By collocating the obtained residual at the
well-known shifted Chebyshev points, we get a system of nonlinear algebraic
equations. In order to obtain a continuous solution, some conditions are added
to the resulting system. Some error bounds are given for the Legendre wavelet
approximation of an arbitrary function. Finally, some examples are included to
show the efficiency and accuracy of this new technique.
