General relativity predicts that gravitational waves propagate at the speed of light. Although ground-based gravitational-wave detectors have successfully constrained the velocity of gravitational waves in the high-frequency range, extending this constraint to the lower frequency range remains a challenge. In this work, we utilize the deviations in the overlap reduction function for a gravitational-wave background within pulsar timing arrays to investigate the velocity of gravitational waves in the nanohertz frequency band. By analyzing the NANOGrav 15-year data set, we obtain a well-constrained lower bound for the velocity of gravitational waves that $v\gtrsim 0.85c$ at the $3\sigma$ credible level, where $c$ is the speed of light.

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• Alternative gravity theories
• Experimental studies of gravity
• Gravitational waves