Abstract
Magnetic field and the fractional Maxwell fluids' impacts on peristaltic flows within a circular cylinder tube with heat transfer was evaluated while assuming that they are preset with a low-Reynolds number and a long wavelength. Utilizing, the fractional calculus method, the problem was solved analytically. It was deduced for temperature, axial velocity, tangential stress, and heat transfer coefficient. Many emerging parameters and their effects on the aspects of the flow were illustrated, and the outcomes were expressed via graphs. A special focus was dedicated to some criteria, such as the wave amplitude's effect, Hartman and Grashof numbers, radius and relaxation-retardation ratios, and heat source, which were under discussions on the axial velocity, tangential stress, heat transfer, and temperature coefficients across one wavelength. Multiple graphs of physical interest were provided. The outcomes state that the effect of the criteria mentioned beforehand (the Hartman and Grashof numbers, wave amplitude, radius ratio, heat source, and relaxation-retardation ratio) were quite evident.