ABSTRACT. In this paper, Ulam stability and data dependence for fractional differential equations with Caputo fractional derivative of order α are studied. We present four types of Ulam stability results for the fractional differential equation in the case of 0 < α < 1 and b = +∞ by virtue of the Henry-Gronwall inequality. Meanwhile, we give an interesting data dependence results for the fracti...

In this paper, we obtain some new Gronwall-Bellman type integral inequalities, and we give an application of our results in the study of boundedness of the solutions of nonlinear integrodifferential equations.

in this paper, we propose a new method for the numerical solution of two-dimensional linear and nonlinear volterra integral equations of the first and second kinds, which avoids from using starting values. an existence and uniqueness theorem is proved and convergence isverified by using an appropriate variety of the gronwall inequality. application of the method is demonstrated for solving the ...

In this paper, we propose a new method for the numerical solution of two-dimensional linear and nonlinear Volterra integral equations of the first and second kinds, which avoids from using starting values. An existence and uniqueness theorem is proved and convergence isverified by using an appropriate variety of the Gronwall inequality. Application of the method is demonstrated for solving the ...

By employing the contraction mapping principle and applying Gronwall-Bellman's inequality, sufficient conditions are established to prove the existence and exponential stability of positive almost periodic solution for nonlinear impulsive delay model of hematopoiesis.

OuIang inequalities and their generalizations have proved to be useful tools in oscillation theory, boundedness theory, stability theory, and other applications of differential and difference equations. A nice introduction to continuous and discrete OuIang inequalities can be found in 1, 2 , and studies in 3–5 give some of their generalizations to multiple integrals and higher-dimensional space...