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In this paper, a variable-coefficient time fractional heat-like and wave-like equation with initial and boundary conditions is solved by the use of variable separation method and the properties of Mittag-Leffler function. As a result, exact solutions are obtained, from which some known special solutions are recovered. It is shown that the variable separation method can also be used to solve some others time fractional heat-like and wave-like equation in science and engineering. [ABSTRACT FROM AUTHOR]

In this paper, a direct algorithm of the exp-function method is proposed for exactly solving non-linear evolution equations. To illustrate the validity and advantages of the algorithm, the Korteweg-de Vries and Jimho-Miwa equations are considered. As a result, exact solutions are obtained. It is shown that the exp-function method with the direct algorithm provides a simpler but effective mathematical tool for constructing exact solutions of non-linear evolution equations in fluids. [ABSTRACT FROM AUTHOR]