This paper addresses the problems of stability a nabla discrete distributed-order dynamical system (NDDS). Firstly, based on proposed generalized definition integral, some related definitions calculus are given. Then, several useful inequalities in sense fractional-order difference extended to cases. Meanwhile, basis and Lyapunov direct method, sufficient conditions guaranteeing asymptotic orig...

The paper studies the exact solution of two kinds generalized Fokker-Planck equations in which integral kernels are given either by distributed order function $k_{1}(t) = \int_{0}^{1} t^{-\mu}/\Gamma(1- \mu) d\mu$ or Prabhakar $k_{2}(\alpha, \gamma; \lambda; t) e^{-\gamma}_{\alpha, 1 - \mu}(\lambda; d\mu$, where is denoted as $e^{-\gamma}_{\alpha, t)$. Both these can be called fading memory fun...

The stability of the nabla discrete distributed-order nonlinear dynamic systems is investigated in this paper. Firstly, a sufficient condition for asymptotic proposed based on Lyapunov direct method. In addition, some properties operators are derived. Based these properties, simpler criterion provided to determine such systems. Finally, two examples given illustrate validity results.