Stability, numerical simulations, and applications of Helmholtz-Duffing fractional differential equations

The Helmholtz-Duffing equation with the Caputo fractional order derivative will be introduced in this article. We employ the fixed point theory to establish the existence and uniqueness results and prove the Hyers-Ulam stability. Drone applications for controlling the synthesis of external forces in torque, angular velocity, and projection served as a source of motivation. In the end, we developed numerical simulations to support our theoretical findings.