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In this article,the fractional derivatives in the sense of modified Riemann-Liouville derivative and the Exp-function method are employed for constructing the exact solutions of nonlinear time fractional partial differential equations in mathematical physics.As a result,some new exact solutions for them are successfully established.It is indicated that the solutions obtained by the Exp-function method are reliable,straightforward and effective method for strongly nonlinear fractional partial equations with modified Riemann-Liouville derivative by Jumarie’s.This approach can also be applied to other nonlinear time and space fractional differential equations.