A generalized fractional ( q , h )–Gronwall inequality and its applications to nonlinear fractional delay ( q , h )–difference systems

Stability of nonlinear h-difference systems with n fractional orders

A generalized Gronwall inequality and its application to a fractional differential equation

This paper presents a generalized Gronwall inequality with singularity. Using the inequality, we study the dependence of the solution on the order and the initial condition of a fractional differential equation. © 2006 Elsevier Inc. All rights reserved.

Generalized Gronwall inequalities and their applications to fractional differential equations

In this paper, we provide several generalizations of the Gronwall inequality and present their applications to prove the uniqueness of solutions for fractional differential equations with various derivatives.

A Krasnoselskii Existence Result For Nonlinear Delay Caputo q—Fractional Difference Equations With Applications to Lotka—Volterra Competition Model∗

In this paper, we investigate the existence of solutions for nonlinear delay Caputo q—fractional difference equations. The main result is proved by means of Krasnoselskii’s fixed point theorem. As an application, we link the conclusion of the main theorem to an existence result for Lotka—Volterra model.

H∞-Optimal Fractional Delay Filters

Fractional delay filters are digital filters to delay discrete-time signals by a fraction of the sampling period. Since the delay is fractional, the intersample behavior of the original analog signal becomes crucial. In contrast to the conventional designs based on the Shannon sampling theorem with the bandlimiting hypothesis, the present paper proposes a new approach based on the modern sample...