Asymptotics and large time behaviors of fractional evolution equations with temporal ψ-Caputo derivative

Zhiqiang Li

Mathematics and Computers in Simulation (MATCOM), 2022, vol. 196, issue C, 210-231

Abstract: This paper devotes to developing the asymptotics and large time behaviors of fractional evolution equations, where the temporal derivative is the ψ-Caputo one of orders α∈(0,1) and α∈(1,2) and fractional Laplacian of order s∈(0,1) is used in the spatial direction. We first derive the solution of convolution form to the considered equation with α∈(0,1) in terms of integral transforms and then prove that it is a classical solution. Next, the asymptotic properties of the solution to this equation are established by Young’s inequality for convolution in the Lp(Rd) and Lp,∞(Rd) norms. In addition, the spatial derivative estimates and large time behavior of the solution are also provided. Finally, the corresponding results for α∈(1,2) are presented in a similar manner.

Keywords: ψ-Caputo derivative; Fractional evolution equation; Special function; Asymptotic behavior; Large time behavior (search for similar items in EconPapers)
Date: 2022
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378475422000362
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:196:y:2022:i:c:p:210-231

DOI: 10.1016/j.matcom.2022.01.023

Access Statistics for this article

Mathematics and Computers in Simulation (MATCOM) is currently edited by Robert Beauwens

More articles in Mathematics and Computers in Simulation (MATCOM) from Elsevier
Bibliographic data for series maintained by Catherine Liu ().