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Eidelman, S.D. and Ko-chubei, A.N. (2004) Cauchy Problems for Fractional Diffusion Equations. J. Differ. Equat., 199, 211-255. https://doi.org/10.1016/j.jde.2003.12.002

has been cited by the following article:

• 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.