Motivated by the objective of improving an understanding of the complex rheological fluid dynamics in fluid engineering and biomedical engineering, we consider the creeping flow of Burgers’ fluid with a fractional model through a peristaltic tube in the present article. Homotopy analysis method is used to solve the problem and obtain the approximate analytical solution in terms of axial velocity, volumetric flow rate, pressure gradient, stream function and mechanical efficiency under the long wavelength approximation. It is assumed that the cross-section of the tube varies sinusoidally along the length of tube. The impacts of fractional parameters, material constants, time and amplitude on the pressure difference, frictional force across one wavelength and trapping, are depicted numerically. It is found that the second material constant helps the flow pattern, whereas the other three material constants resist it through the peristaltic tube. The effects of fractional parameters on flow pattern are found to be opposite to each other.