bellman’s inequality
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Author(s):  
Ahmed A. Hamoud

In this paper, we established some new results concerning the uniqueness and Ulam’s stability results of the solutions of iterative nonlinear Volterra-Fredholm integro-differential equations subject to the boundary conditions. The fractional derivatives are considered in the Caputo sense. These new results are obtained by applying the Gronwall–Bellman’s inequality and the Banach contraction fixed point theorem. An illustrative example is included to demonstrate the efficiency and reliability of our results


2015 ◽  
Vol 2015 ◽  
pp. 1-10
Author(s):  
Pan Wang ◽  
Qingmei Lin ◽  
Yongkun Li

We consider an impulsive stochastic host-macroparasite equation on time scales. By use of the Banach fixed point theorem and Gronwall-Bellman’s inequality technique on time scales, we obtain the existence and exponential stability of mean-square almost periodic solutions for the host-macroparasite equation on time scales. Finally, we give an example to illustrate the feasibility of our results.


2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Jing-Feng Tian ◽  
Shu-Yan Wang

We give some refinements of generalized Aczél's inequality and Bellman's inequality proposed by Tian. As applications, some refinements of integral type of generalized Aczél's inequality and Bellman's inequality are given.


2010 ◽  
Vol 15 (4) ◽  
pp. 505-516 ◽  
Author(s):  
Gani Tr. Stamov ◽  
Jehad O. Alzabut

In this paper, sufficient conditions are established for the existence of almost periodic solutions for system of impulsive integro‐differential neural networks. Our approach is based on the estimation of the Cauchy matrix of linear impulsive differential equations. We shall employ the contraction mapping principle as well as Gronwall‐Bellman's inequality to prove our main result. The research of Gani Tr. Stamov is partially supported by the Grand 100ni087–16 from Technical University–Sofia


1995 ◽  
Vol 229 ◽  
pp. 9-14
Author(s):  
Changqin Xu

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