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In this paper, we investigate the unified method and the modified Kudryashov method for obtaining exact traveling wave solutions of conformable fractional partial differential equations. In addition, a connection is given between the two methods. Then, using these methods, we obtain new exact solutions for the space-time fractional (2 + 1)-dimensional Calogero-Bogoyavlensky-Schiff equation. Fractional derivatives are described in conformable sense. Various solutions have been obtained, including one-soliton, kink, anti-kink, periodic wave solutions, and multiple-soliton solutions. We also provide a graphical representation of some interesting exact solutions to the equation and discuss the behavior of these solutions. The considered methods can be effectively applied to a wide range of nonlinear fractional partial differential equations. [ABSTRACT FROM AUTHOR]

In this paper, we study the oscillatory properties for asymptotic behaviors of solutions of a class of nonlinear second-order stochastic Itô equations. Meanwhile, we investigate existence of zeros of its solutions with probability 1. Sufficient conditions for the oscillation and nonoscillation of solutions are obtained on the half-line [t0,∞) for every t0 > 0. [ABSTRACT FROM AUTHOR]

We study an asymptotic behavior of solutions of a nonlinear system by comparing with a linear system, whose asymptotic behavior of solutions is similar to the behavior of solutions of the original system. [ABSTRACT FROM AUTHOR]

In this work we establish the connection between the invariant sets of the systems of differential equations and the corresponding systems of difference equations in terms of the zeros of positively definite Lyapunov's functions. [ABSTRACT FROM AUTHOR]