Claudio Cuevas

S-asymptotically ω-periodic solutions of semilinear fractional integro-differential equations

Abstract We study S -asymptotically ω -periodic solutions of the semilinear fractional equation u ′ = ∂ − α + 1 A u + f ( t , u ) , 1 α 2 , considered in a Banach space X , where A is a linear operator of sectorial type μ 0 .

Almost automorphic solutions to a class of semilinear fractional differential equations

Abstract We study almost automorphic (mild) solutions of the semilinear fractional equation ∂ t α u = A u + ∂ t α − 1 f ( ⋅ , u ) , 1 α 2 , considered in a Banach space X , where A is a linear operator of sectorial type ω 0 . We prove the existence and uniqueness of an almost automorphic mild solution assuming that f ( t , x ) is almost automorphic in t for each x ∈ X , satisfies some Lipschitz type conditions and takes values on X .

On Type of Periodicity and Ergodicity to a Class of Fractional Order Differential Equations

We study several types of periodicity to a class of fractional order differential equations.

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.

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

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

Almost periodic and pseudo-almost periodic solutions to fractional differential and integro-differential equations

Abstract We study the existence of almost periodic (resp., pseudo-almost periodic) mild solutions for fractional differential and integro-differential equations in the case when the forcing term belongs to the class of Stepanov almost (resp., Stepanov-like pseudo-almost) periodic functions.

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.

Weighted S-Asymptotically ω-Periodic Solutions of a Class of Fractional Differential Equations

We study the existence of weighted -asymptotically -periodic mild solutions for a class of abstract fractional differential equations of the form , where is a linear sectorial operator of negative type.We study the existence of weighted Open image in new window -asymptotically Open image in new window -periodic mild solutions for a class of abstract fractional differential equations of the form Open image in new window , where Open image in new window is a linear sectorial operator of negative type.

Asymptotically periodic solutions of fractional differential equations

Abstract We study the existence of pseudo S -asymptotically ω -periodic mild solutions for a class of abstract fractional differential equation.

On Well-Posedness of Difference Schemes for Abstract Elliptic Problems in Lp([0, T];E) Spaces

This paper is devoted to the numerical analysis of abstract elliptic differential equations in L p ([0, T];E) spaces. The presentation uses general approximation scheme and is based on C 0-semigroup theory and a functional analysis approach. For the solutions of difference scheme of the second-order accuracy, the almost coercive inequality in spaces with the factor is obtained. In the case of UMD space E n , we establish a coercive inequality for the same scheme in under the condition of R-boundedness.