  The muon $g-2$ anomaly is a long-standing discrepancy from its standard model
prediction. The recent improved measurement of the fine structure constant
makes the electron $g-2$ anomaly very interesting for both sign and magnitude
in comparison to the muon $g-2$ anomaly. In order to explain both muon and
electron $g-2$ anomalies, we introduce flavor violation in the minimal
supersymmetric standard model (MSSM) as a low energy theory. The lepton flavor
violating process $\tau \to e\gamma$ is one the major constraints to explain
both $g-2$ anomalies simultaneously emerging from flavor violating terms. We
show various mass spectra of sleptons, neutralinos, and charginos, consistent
with the LHC results, to explain both anomalies after satisfying the flavor
violation constraint.
