Fractional Retarded Differential Equations Involving Mixed Nonlocal Plus Local Initial Conditions. (26th October 2019)

• Record Type: Journal Article
• Authors: Zhang, Xuping; Chen, Pengyu; Li, Yongxiang
• Is Part Of: Numerical functional analysis and optimization. Volume 40:Number 14(2019)
• Page Start: 1678
• Page End: 1702
• Publication Date: 2019-10-26
• Subjects: Convex-condensing operator -- equicontinuous semigroup -- fractional delay evolution equations -- Kuratowski measure of noncompactness -- nonlocal delay initial condition; 26A33 -- 34K30 -- 47D06 -- 47G20; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2019.1639728
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: The aim of this paper is to discuss the existence of mild solutions and positive mild solutions for a general class of semilinear fractional retarded evolution equations subjected to mixed nonlocal plus local initial conditions on infinite dimensional Banach spaces. Under the situation that the nonlinear term and nonlocal function satisfy some appropriate growth conditions and a noncompactness measure condition, we obtained the existence of mild solutions and positive mild solutions by utilizing a generalized Darbo's fixed point theorem and a new estimation technique of the measure of noncompactness. In addition, the strong restriction on the constants in the condition of noncompactness measure is completely deleted in this paper. An example about the retarded parabolic partial differential equation involving a general mixed nonlocal plus local initial conditions is also given to illustrate the feasibility of our abstract results.