A map-type Gronwall inequality on functional differential equations with state-dependence

Existence and continuous dependence for fractional neutral functional differential equations

In this paper, we investigate the existence, uniqueness and continuous dependence of solutions of fractional neutral functional differential equations with infinite delay and the Caputo fractional derivative order, by means of the Banach's contraction principle and the Schauder's fixed point theorem.

A New Generalized Gronwall-Bellman Type Inequality

On Gronwall Inequality

In this paper, we obtained some new Gronwall-Bellman type integral inequalities and we give some consequences of our results.

On impulsive fuzzy functional differential equations

In this paper, we prove the existence and uniqueness of solution to the impulsive fuzzy functional differential equations under generalized Hukuhara differentiability via the principle of contraction mappings. Some examples are provided to illustrate the result.

On an Inequality of Gronwall

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.