Abstract Unexpected sign, significant magnitude and variable frequency second derivative exists not only in singular radio pulsars but also in Soft Gamma repeaters (SGRs) and Anomalous X-ray pulsars (AXPs). This paper shows that these phenomena are related, and can be interpreted by a simple unified model, long-term orbital effect. Thus many of previous ``isolated'' pulsars may be binary pulsars, i.e., orbital period Pb≈(47,72)min for AXP 1E 2259+586, and Pb≈(20,34)min for PSR J1614–5047, Pb≈(3.6,6.4)min for SGR 1900+14, and Pb≈(1.5,5.8)min for SGR 1806–20. In this model, the frequency first derivative of these pulsars is still dominated by magnetic dipole radiation. Therefore, it is not contradictory to the magnetar interpretation of SGRs and AXPs. In other words, the model of this paper provides new interpretation to higher order of derivatives of pulse frequency (second and third...) instead of the first.
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