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According to the inflationary model, the universe had a brief period of extraordinarily rapid expansion or inflation during which its diameter increased by a factor at least 1025 times larger than previously thought. In this work an analysis is given on inflationary universe, which expands at a rate intermediate between that of power-law and exponential inflation. We have examined the model of Barrow which is solved exactly and leaded to power law inflation. We have tested a new potential by applying the scalar field using the equation of motion and found some new interior solutions. The Chittagong Univ. J. Sci. 40(1) : 112-121, 2019