TITLE:
Solvability of Nonlinear Sequential Fractional Dynamical Systems with Damping
AUTHORS:
Cuie Xiao, Xiuwen Li
KEYWORDS:
Solvability, Sequential Fractional Equations, Mittag-Leffler Function, Gramian matrix, Fixed Point Theorems
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.5 No.2,
February
15,
2017
ABSTRACT:
In this paper, we are concerned with the solvability for a class of nonlinear sequential fractional dynamical systems with damping infinite dimensional spaces, which involves fractional Riemann-Liouville derivatives. The solutions of the dynamical systems are obtained by utilizing the method of Laplace transform technique and are based on the formula of the Laplace transform of the Mittag-Leffler function in two parameters. Next, we present the existence and uniqueness of solutions for nonlinear sequential fractional dynamical systems with damping by using fixed point theorems under some appropriate conditions.