Application of the simplest equation method to some time-fractional partial differential equations

A novel analytical method for time-fractional differential equations

“…For this reason, in recent years, several e¤ective mathematical methods have been proposed to obtain solutions of NFDEs. Such as the ( G 0 G )-expansion method [4,5,6], exp-rational function method [7], exp-function method [8,9], the modi…ed simple equation method [10], the generalized Kudryashov method [11], the …rst integral method [12], the simplest equation method [13], the functional variable method [14], sub-equation method [15], ansatz method [16,17], trial equation method [18] and so on [19]. The common of these analytical methods is based on the homogenous balance principle.…”

The modified simple equation method for solving some fractional-order nonlinear equations

“…Note: Comparing our solutions with [30,31], it can be seen that by choosing suitable values for the parameters, similiar solutions can be verified (figure 2).…”

“…As FDEs appear more and more frequently in various research and engineering applications, such as signal processing, control theory, viscoelasticity, biology, physics and electrochemistry (see refs [1][2][3][4][5][6] and references therein), they attract considerable interest and there has been a significant theoretical development recently (for example, see refs [2,4,5]). Also many powerful methods, for example, exponential function method [7,8], (G /G)-expansion method [9,10], first integral method [11,12], subequation method [13,14], functional variable method [15,16], modified simple equation method [17], modified trial equation method [18] and so on [19] have been proposed to obtain exact solutions of fractional differential equations.…”

Analytical Approach for the Space-time Nonlinear Partial Differential Fractional Equation

“…Recently, several mathematical methods including the fractional G 0 G À Á -expansion method [4,5,6,7], the fractional exp-function method [8,9,10,11], the fractional first integral method [12,13], the fractional subequation method [14,15,16], the fractional fractional functional variable method [17], the fractioanal modified trial equation method [18,19], fractional characteristics method [21], direct algebraic method [22] and the fractional simplest equation method [23] have been developed to obtain exact analytic solutions. Using these methods, solutions with various forms for given fractional differential equation have been established.…”