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Employing the Quark Mass Denisity- and temperature- dependent model and theHartle's method, We have studied the slowly rotating strange star with uniformangular velocity. The mass-radius relation, the moment of inertia and the framedragging for different frequencies are given. We found that we cannot use thestrange star to solve the challenges of Stella and Vietri for the horizontalbranch oscillations and the moment of inertia $I_{45}/(M/M_ s)>2.3$.Furthermore, we extended the Hartle's method to study the differential rotatingstrange star and found that the differential rotation is an effective way toget massive strange star.Comment: Latex file, 13 figures, accepted for publication in Inter. J. Mod.  Phys.

SLOWLY ROTATING PROTO STRANGE STARS IN QUARK MASS DENSITY- AND TEMPERATURE-DEPENDENT MODEL