On the attractivity of solutions for a class of multi-term fractional functional differential equations

Abstract

Please cite this article as: J. Losada, J.J. Nieto, E. Pourhadi, On the attractivity of solutions for a class of multi-term fractional functional differential equations, Journal of Computational and Applied Mathematics (2015), http://dx. AbstractIn this paper, we present some alternative results concerning with the existence and attractivity dependence of solutions for a class of nonlinear fractional functional differential equations. In our consideration, we apply the well-known Schauder fixed point theorem in conjunction with the technique of measure of noncompactness. Moreover, we provide some examples to illustrate the effectiveness of the obtained results. (2010): 47H10; 34A08. Keywords: Schauder fixed point theorem; attractive solutions; fractional functional differential equations; measure of noncompactness. Mathematics Subject Classification

On the PC $\mathcal{PC}$ -mild solutions of abstract fractional evolution equations with non-instantaneous impulses via the measure of noncompactness

“…As a part of their investigation, the existence of mild solutions on R + and the existence of S-asymptotically ω-periodic mild solutions based on the Hausdorff measure of noncompactness have been established. We remark that the measure of noncompactness has been recently utilized in several papers (for example, see [2,27]). Both integer-or fractional-order differential equations with impulses have been studied previously.…”

Eigenvalue problems for nonlinear conformable fractional differential equations with multi-point boundary conditions

“…Jiang 12 obtained the eigenvalue interval for multi-point boundary value problems of fractional differential equations. By using some properties of the classical Mittag-Leffler functions, Nieto 13 presented two new maximum principles for a linear fractional differential equation with initial or periodic boundary conditions. Based on Krasnosel'skii and Schauder fixed point theorems and monotone iterative technique, the authors 14 studied existence and uniqueness of periodic solutions for a particular class of nonlinear fractional differential equations admitting its righthand side with certain singularities.…”

Existence and Attractivity for Fractional Evolution Equations

“…Recently, Zhou [7], Chen et al [19], Losada et al [20], and Banaś and O'Regan [21] investigated the attractivity of solutions for fractional ordinary differential equations and integral equations. On the other hand, the existence theory of solutions for time fractional evolution equations has been investigated intensively by many authors; for example, see Kim et al [16], Bazhlekova [22], Wang et al [23], Zacher [24], and Zhou et al [25].…”