The occurrence of horseshoe chaos in Duffing oscillator with fractional damping and multi-frequency excitation is analyzed by using analytical and numerical techniques. Applying Melnikov method, analytical threshold condition for the onset of horseshoe chaos is obtained. The effect of damping exponent and the number of periodic forces on the dynamics of the Duffing oscillator is also analyzed. Due to fractional damping and multi-frequency excitation, suppression of chaos and various nonlinear phenomena are predicted. Analytical predictions are demonstrated through numerical simulations.