Global existence and decay of solutions for the generalized bad Boussinesq equation

Construction of Fractional Power Series Solutions to Fractional Boussinesq Equations Using Residual Power Series Method

“…(2) a linear description of irregular waves based on superposition of individual frequency components with random phases [17,18]. So many mathematicians and physicists tried to contract new model to describe the process of wave propagation on the surface of water.…”

“…So many mathematicians and physicists tried to contract new model to describe the process of wave propagation on the surface of water. In 1872, the French scientist Joseph Boussinesq (1842-1929) derived a model equation [18]…”

“…was applied to problems not only in the study of the dynamics of thin inviscid layers with free surface but also in the study of nonlinear string, the shape-memory alloys, the propagation of waves in elastic rods, shallow wave waters (waves with long wavelength compared to the depth), and the continuum limit of lattice dynamics or coupled electrical circuits. More and more researchers pay attention to this equation and get a number of interesting results which were applied to many areas [17][18][19][20]. In recent years, with the development of fractional system rapidly, the classical Boussinesq equation evolves into the fractional Boussinesq equation, which is suitable for studying the water propagation through heterogeneous porous media [21][22][23][24].…”