University of Guilan Journal of Mathematical Modeling 2345-394X 7 3 2019 09 01 Horseshoe dynamics in Duffing oscillator with fractional damping and multi-frequency excitation 263 276 3466 10.22124/jmm.2019.12719.1242 EN S. Valli Priyatharsini Department of Physics, Sadakathullah Appa College, Tirunelveli-627 011, Tamil Nadu, India (Affliated to Manonmaniam Sundaranar University, Tirunelveli-627012, Tamil Nadu, India) M.V Sethu Meenakshi Department of Mathematics, St. Xavier's College, Tirunelveli -627 002, Tamil Nadu, India V. Chinnathambi Department of Physics, Sadakathullah Appa College, Tirunelveli-627 011, Tamil Nadu, India (Affliated to Manonmaniam Sundaranar University, Tirunelveli-627012, Tamil Nadu, India) S. Rajasekar School of Physics, Bharathidasan University, Tiruchirapalli-620 024, Tamil Nadu, India Journal Article 2019 03 07 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. https://jmm.guilan.ac.ir/article_3466_b6643df11026c9c69b92a381009e3107.pdf