On the invariant solutions of space/time-fractional diffusion equations

Symmetry properties and exact solutions of the time fractional Kolmogorov-Petrovskii-Piskunov equation

“…Here, some description for solving fractional partial differential equations (FPDEs) via Lie symmetry analysis will be provided. Surmise that FPDE having as in [16][17][18][19][20][21][22][23][24][25][26]]…”

Invariant Solutions and Conservation Laws of the Time-Fractional Telegraph Equation

“…To obtain new infinitesimal generators of a fractional differential equation and new solutions, we use the class of conditional symmetries or the so-called nonclassical symmetry method, which is proposed by Bluman and Cole [34] for the first time. A number of investigators have applied the method to find analytical solutions for the fractional differential equations [35][36][37][38][39][40]. Conservation laws have a crucial role in the mathematical physics.…”

Approximate analytical solutions of non-linear local fractional heat equations

“…where k is a constant, ∂ α u /∂t α and ∂ 2β u /∂x 2β are the local fractional derivatives [1][2][3][4][5] (0 < α ≤ 1, 0 < β ≤ 1), φ(x) and f(x, t) are given functions. The classical heat equation is one of the most important PDE to model problems in mathematical physics [6][7][8][9][10][11][12][13][14][15]. The non-linear local fractional heat equation can be used to model the fractal electromagnetic radiation, the fractal seismology, the fractal acoustics and so on [1][2][3][4][5].…”