Discrete Gronwall’s inequality for Ulam stability of delay fractional difference equations by Shu-Yu Yang, Guo-Cheng Wu

Subjects: Get full text

On some new N-independent-variable discrete inequalities of the Gronwall type by En Hao Yang

“…In this paper we shall establish some new discrete inequalities of the Gronwall type in N-independent variables. …”
Get full text

Some New Discrete Gronwall-Bellman Type Inequalities with Three Independent Variables and Applications by Weihua Liu, Haisong Huang

“…Some new discrete Gronwall-Bellman type inequalities with three independent variables which generalize some existing results and can be used as handy tools in the study of qualitative and quantitative properties of solutions of certain classes of difference equation are presented. …”
Get full text

Some Nonlinear Integral Inequalities Connected with Retarded Terms on Time Scales by Zareen A. Khan, Hijaz Ahmad, Saima Rashid, Kadir Kaynak, Miao-Kun Wang

“…The objective of this research is to formulate a specific class of integral inequalities of Gronwall kind concerning retarded term and nonlinear integrals with time scales theory. …”
Get full text

About Total Stability of a Class of Nonlinear Dynamic Systems Eventually Subject to Discrete Internal Delays by Manuel De la Sen

“…The results are based on the ad hoc use of Gronwall’s inequality.…”
Get full text

Least Squares Estimation for Discretely Observed Stochastic Lotka–Volterra Model Driven by Small α-Stable Noises by Chao Wei, Yan Wei, Yingying Zhou

Get full text

Linear Control of Fractional-Order Financial Chaotic Systems with Input Saturation by Junhai Luo, Guanjun Li, Heng Liu

Get full text

Finite-Time Stability of Solutions for Nonlinear q-Fractional Difference Coupled Delay Systems by Jingfeng Wang, Chuanzhi Bai

“…In this paper, we investigate and prove a new discrete q-fractional version of the coupled Gronwall inequality. …”
Get full text

Boundedness of the Solutions to Certain Delay Dynamic Integrodifferential Systems on Time Scales by Min Fan, Yazhou Tian

Get full text

Uniqueness and Novel Finite-Time Stability of Solutions for a Class of Nonlinear Fractional Delay Difference Systems by Danfeng Luo, Zhiguo Luo

Get full text

On approximation of the solutions of delay differential equations by using piecewise constant arguments by Istevan Györi

“…We also consider the delay differential equations of neutral type by applying a generalization of the Gronwall Bellman inequality.…”
Get full text

An Efficient Hybrid Numerical Scheme for Nonlinear Multiterm Caputo Time and Riesz Space Fractional-Order Diffusion Equations with Delay by A. K. Omran, M. A. Zaky, A. S. Hendy, V. G. Pimenov

“…The problem is first approximated by the L1 difference method on the temporal direction, and then, the Galerkin–Legendre spectral method is applied on the spatial discretization. Armed by an appropriate form of discrete fractional Grönwall inequalities, the stability and convergence of the fully discrete scheme are investigated by discrete energy estimates. …”
Get full text