Existence and exact controllability of fractional evolution inclusions with damping. (2nd February 2017)

• Record Type: Journal Article
• Authors: Li, Xiuwen; Liu, Zhenhai; Tisdell, C. C.
• Is Part Of: Mathematical methods in the applied sciences. Volume 40:Number 12(2017)
• Page Start: 4548
• Page End: 4559
• Publication Date: 2017-02-02
• Subjects: existence -- exact controllability -- fractional inclusions -- damping -- regularized resolvent family; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.4325
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : The aim of this paper is to deal with the existence of mild solutions and exact controllability for a class of fractional evolution inclusions with damping (FEID, for short) in Banach spaces. Firstly, we provide the representation of mild solutions for FEID by applying the method of Laplace transform and the theory of ( α, κ )‐regularized families of operators. Next, we are concerned with the existence and exact controllability of FEID under some suitable sufficient conditions by using the method of measure of noncompactness and an appropraite fixed point theorem. Finally, an application to nonlinear partial differential equations with temporal fractional derivatives is presented to illustrate the effectiveness of our main results. Copyright © 2017 John Wiley & Sons, Ltd.