Time fractional evolution of two superconducting charge qubits

We investigate the quantum correlation dynamics between two superconducting charge qubits (TSC-Q), governed by the time-fractional Schrödinger equation (TFSE), a framework incorporating non-Markovian memory effects arising from environmental interactions. By analyzing separable and partially entangled initial states, we highlight the central role of the fractional order $\tau$, Josephson energies ($E_{J1}$, $E_{J2}$), and coupling strength ($E_m$) in modulating concurrence, quantum steering asymmetry, and Bell nonlocality (via the CHSH inequality). Our results indicate that a decrease in the value of $\tau$ promotes a faster generation of quantum correlations for separable and partially entangled states, highlighting the dual role of $\tau$ as both a catalyst and a stabilizer of quantum resources. Furthermore, it is important to note that optimal behavior of quantum correlations is observed when the Josephson energies of the two qubits are close, i.e., when $E_{J2}\approx E_{J1}$. In addition, a stronger coupling strength, denoted by $E_m$, further enhances the generation of these correlations. The synergy among $\tau$, $E_{J1}$, $E_{J2}$, and $E_m$ defines a tunable parameter space for engineering memory-driven correlations to mitigate decoherence. These results position the TFSE as a promising tool for modeling non-Markovian dynamics in superconducting architectures, paving the way for robust quantum platforms with enhanced correlations, suitable for scalable quantum computing and secure communication systems.