Multiple Integration of the Heat-Conduction Equation for a Space Bounded From the Inside

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].…”

Application of DGJ method for solving non-linear local fractional heat equations

“…The solution of the local fractional differential equation is much involved. Some numerical and analytical methods for solving local fractional differential equations were presented [5][6][7][8][9][10][14][15][16][17][18], such as the fractional complex transform method and the DGJ method. Fractional complex transform can convert the fractional differential equation into the ODE [11,12].…”