Bäcklund transformation of fractional Riccati equation and its applications to nonlinear fractional partial differential equations

Space-time fractional Rosenou-Haynam equation: Lie symmetry analysis, explicit solutions and conservation laws

“…FDEs have been studied nowadays to describe several physical aspects and procedure in natural conditions [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]. However, fractional partial differential equations (FPDEs) having only time derivative have been analyzed via the Lie symmetry method [20][21][22][23][24][25][26].…”

Lie symmetry analysis and conservation laws for the time fractional simplified modified Kawahara equation

“…Lie's method is one of the global and e cient methods for investigating analytical solutions and symmetry properties of nonlinear partial di erential equations (NLPDEs) [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17]. Fractional calculus has been successfully used to explain many complex nonlinear phenomena and dynamic processes in physics, engineering, electromagnetics, viscoelasticity, and electrochemistry [18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34].…”

The Backlund Transformation of the Generalized Riccati Equation and Its Applications to the Nonlinear KPP Equation

“…Nonlinear wave phenomena of dispersion, dissipation, diffusion, reaction and convection are very important in nonlinear wave equations. In recent decades, many effective methods have been established to obtain exact solutions of nonlinear PDEs, such as the inverse scattering transform [1], the Hirota method [2], the truncated Painlevé expansion method [3], the Bäcklund transform method [1,4,5], the exp-function method [6][7][8], the simplest equation method [9,10], the Weierstrass elliptic function method [11], the Jacobi elliptic function method [12][13][14], the tanh-function method [15,16], the ( / G) G′ expansion method [17][18][19][20][21][22], the modified simple equation method [23][24][25][26], the Kudryashov method [27][28][29], the multiple exp-function algorithm method [30,31], the transformed rational function method [32], the Frobenius decomposition technique [33], the local fractional variation iteration method [34], the local fractional series expansion The objective of this article is to use the Bäcklund transformation of the generalized Riccati equation to construct new exact traveling wave solutions of the following nonlinear Kolmogorov-Petrovskii-Piskunov (KPP) equation [22,26,46]. [22] have discussed Equation (1.1) using the ( / G) G′ -expansion method and found its ex...…”