José Paulo Carvalho dos Santos

Existence results for fractional neutral integro-differential equations with state-dependent delay

In this paper we study the existence of mild solutions for a class of abstract fractional neutral integro-differential equations with state-dependent delay. The results are obtained by using the Leray-Schauder alternative fixed point theorem. An example is provided to illustrate the main results.

On state-dependent delay partial neutral functional integro-differential equations

In this paper the existence of mild solutions for a class of abstract neutral integro-differential equations with state-dependent delay is studied.

Asymptotically almost automorphic solutions of abstract fractional integro-differential neutral equations

We study asymptotically almost automorphic solutions of abstract fractional integro-differential neutral equations.

Existence Results for a Fractional Equation with State-Dependent Delay

We provide sufficient conditions for the existence of mild solutions for a class of abstract fractional integrodifferential equations with state-dependent delay. A concrete application in the theory of heat conduction in materials with memory is also given.

Asymptotically Almost Periodic Solutions for Abstract Partial Neutral Integro-Differential Equation

The existence of asymptotically almost periodic mild solutions for a class of abstract partial neutral integro-differential equations with unbounded delay is studied.

Existence of S-asymptotically ω-periodic solutions to abstract integro-differential equations

We study the existence of solutions for a class of abstract equations.We construct an exponentially stable resolvent operator.Solutions S-asymptotically ω-periodic are obtained.We obtained existence results with less restrictions on the constants.We provide a concrete example for the abstract results. The main aim of this work is to study the existence of S-asymptotically ω-periodic solutions for a class of abstract integro-differential equations modeled in the following form d dt x ( t ) + ? 0 t N ( t - s ) x ( s ) ds ] = Ax ( t ) + ? 0 t B ( t - s ) x ( s ) ds + f ( t , x ( t ) ) , t ? 0 , x ( 0 ) = x 0 ? X , where A , B ( t ) for t ? 0 are closed linear operators defined on a common domain D ( A ) which is dense in X , N ( t ) for t ? 0 are bounded linear operators on X, and f : 0 , ∞ ) i? X ? X is an appropriate function. The existence results are obtained by applying the theory of exponentially stable resolvent operators. We also discuss an application of these results.

A Fractional-Order Epidemic Model for Bovine Babesiosis Disease and Tick Populations

This paper shows that the epidemic model, previously proposed under ordinary differential equation theory, can be generalized to fractional order on a consistent framework of biological behavior. The domain set for the model in which all variables are restricted is established. Moreover, the existence and stability of equilibrium points are studied. We present the proof that endemic equilibrium point when reproduction number is locally asymptotically stable. This result is achieved using the linearization theorem for fractional differential equations. The global asymptotic stability of disease-free point, when , is also proven by comparison theory for fractional differential equations. The numeric simulations for different scenarios are carried out and data obtained are in good agreement with theoretical results, showing important insight about the use of the fractional coupled differential equations set to model babesiosis disease and tick populations.

Global stability of fractional SIR epidemic model

In this work, we prove the global stability of endemic and free disease equilibrium points of the Fractional SIR model using comparison theory of fractional differential inequality and fractional La-Salle invariance principle for fractional differential equations.

A generalized Mittag-Leffler function to describe nonexponential chemical effects

Abstract In this paper a differential equation with noninteger order was used to model an anomalous luminescence decay process. Although this process is in principle an exponential decaying process, recent data indicates that is not the case for longer observation time. The theoretical fractional differential calculus applied in the present work was able to describe this process at short and long time, explaining, in a single equation, both exponential and nonexponential decay process. The exact solution found by fractional model is given by an infinite series, the Mittag-Leffler function, with two adjusting parameters. To further illustrate this nonexponential behavior and the fractional calculus framework, an stochastic analysis is also proposed.