In this paper, we study the Adomian decomposition method (ADM for short) including its iterative scheme and convergence analysis, which is a simple and effective technique in dealing with some nonlinear problems. We take algebraic equations and fractional differential equations as applications to illustrate ADM’s efficiency.
We study a type of iterative method and apply it to time-fractional Swift-Hohenberg equation with initial value. Using this iterative method, we obtain the approximate analytic solutions with numerical figures to initial value problems, which indicates that such iterative method is effective and simple in constructing approximate solutions to Cauchy problems of time-fractional differential equations.
In this paper, we discuss the dynamics of a stochastic SIQS epidemic model. When the noise is large, the infective decays exponentially to zero regardless of the magnitude of R 0 . When the noise is small, sufficient conditions for extinction exponentially and persistence in the mean are established. The results are illustrated by computer simulations. MSC: 34F05; 37H10; 60H10; 92D25; 92D30
This paper focuses on the asymptotic solutions to time-space fractional coupled systems, where the fractional derivative and integral are described in the sense of Caputo derivative and Riemann-Liouville integral. We introduce the Residual Power Series (for short RPS) method to construct the desired asymptotic solutions. Furthermore, we apply this method to some time-space fractional coupled systems. The simplicity and efficiency of RPS method are shown by the application.
In this article, we study the boundary value problems for the fourth-order nonlinear coupled difference equationsThroughout our nonlinearity may be singular. We establish the existence of positive solutions for the fourth-order coupled systems. The proof relies on Schauder's fixed point theorem. MSC: 39A11
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