Tran Dinh Ke

Decay integral solutions for a class of impulsive fractional differential equations in Banach spaces

The aim of this paper is to establish the existence of decay integral solutions to a class of retarded fractional differential equations involving impulsive effects. The results are obtained by using the fixed point approach and fractional calculus tools in Banach spaces. Applications to both ordinary and partial differential equations are presented.

Decay solutions for a class of fractional differential variational inequalities

Abstract Our aim is to study a new class of differential variational inequalities involving fractional derivatives. Using the fixed point approach, the existence of decay solutions to the mentioned problem is proved.

Stability for a class of fractional partial integro-differential equations

In this paper, we deal with a class of fractional integro-differential equations involving impulsive effects and nonlocal conditions, whose principal part is of diffusion-wave type. Our aim is to establish some existence and stability results for integral solutions to the mentioned problem by fixed point approach.

On a class of fractional order differential inclusions with infinite delays

Our aim is to study fractional order differential inclusions with infinite delays in Banach spaces. We impose the regularity condition on multivalued nonlinearity in terms of measures of noncompactness to get the existence result. Some properties of the solution map are proved.

On Semilinear Integro-Differential Equations with Nonlocal Conditions in Banach Spaces

We study the abstract Cauchy problem for a class of integrodifferential equations in a Banach space with nonlinear perturbations and nonlocal conditions. By using MNC estimates, the existence and continuous dependence results are proved. Under some additional assumptions, we study the topological structure of the solution set.

Long-time behaviour for a model of porous-medium equations with variable coefficients

By analysing the uniform attractor for multi-valued processes, we study the long-time behaviour of the solutions of a model of non-autonomous porous-medium equations. The result is obtained by using the a priori estimates and suitable compactness arguments.

Power-Rate Synchronization of Fractional-Order Nonautonomous Neural Networks with Heterogeneous Proportional Delays

This paper is concerned with the problem of global power-rate synchronization of fractional-order nonautonomous neural networks with heterogeneous proportional delays. By utilizing the Leibniz rule for fractional differentiation and an extended comparison technique, delay-dependent conditions are derived to ensure that the considered fractional-order neural network model is globally synchronous with a power decaying rate. Two examples with numerical simulations are given to demonstrate the effectiveness of the obtained results.

Pullback attractor for differential evolution inclusions with infinite delays

We analyze the existence of pullback attractor for non-autonomous differential inclusions with infinite delays in Banach spaces by using measures of noncompactness. The obtained results can be applied to control systems driven by semilinear partial differential equations and multivalued feedbacks.

Asymptotic behavior for nonautonomous functional differential inclusions with measures of noncompactness

We study the asymptotic behavior of nonautonomous differential inclusions with delays in Banach spaces by analyzing their pullback attractors. Our aim is to give a recipe expressed by measures of noncompactness to prove the asymptotic compactness of the process generated by our system. This approach is effective for various differential systems regardless of the compactness of the semigroup governed by linear part.