The Differential Operators of Order 1 + alpha and their Integral Counterpart; Existence and Uniqueness of Solution for the Differential Equations of Order alpha Position of the Zeros, the Bihari Inequality, and the Asymptotic Behavior of Solutions for the Differential Equations of Order alpha Asymptotic Integration for the Differential Equations of Order 1 + alpha Existence and Uniqueness of Solution for Some Delay Differential Equations with Caputo Derivatives; Existence of Positive Solutions for some Delay Fractional Differential Equations with a Generalized N-Term; Stability of a Class of Discrete Fractional Non-autonomous Systems; Mittag-Leffler Stability for Fractional Nonlinear Systems with Delay; A Razumikhin Stability Theorem for Fractional Systems with Delay; Controllability of Fractional Evolution Non-Local Impulsive Quasilinear Delay Integro-Differential Systems; Approximate Controllability of Sobolev Type Nonlocal Fractional Stochastic Dynamic Systems in Hilbert Spaces;