In this manuscript, a new fractional-order (FO) oscillator is proposed, which employs two fractional-order capacitors (FOC) and two operational trans-conductance amplifiers (OTA). The difference of phase between two output voltages of FO oscillator can be independently controlled. Sensitivity of frequency of oscillations with respect to different circuit parameters is drafted mathematically. The functionality of the proposed structure is confirmed through SPICE simulations with 180nm CMOS technology model parameters and stability of the same is confirmed through pole plot in W-plane using forlocus function of MATLAB. Corner analysis and Monte-Carlo analysis are also carried out to illustrate the robustness of the proposed FO oscillator.