Fractional Evolution Equations with Infinite Time Delay in Abstract Phase Space

Ahmed Salem, Kholoud N. Alharbi and Hashim M. Alshehri
Additional contact information
Ahmed Salem: Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
Kholoud N. Alharbi: Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
Hashim M. Alshehri: Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia

Mathematics, 2022, vol. 10, issue 8, 1-17

Abstract: In the presented research, the uniqueness and existence of a mild solution for a fractional system of semilinear evolution equations with infinite delay and an infinitesimal generator operator are demonstrated. The generalized Liouville–Caputo derivative of non-integer-order 1 < α ≤ 2 and the parameter 0 < ρ < 1 are used to establish our model. The ρ -Laplace transform and strongly continuous cosine and sine families of uniformly bounded linear operators are adapted to obtain the mild solution. The Leray–Schauder alternative theorem and Banach contraction principle are used to demonstrate the mild solution’s existence and uniqueness in abstract phase space. The results are applied to the fractional wave equation.

Keywords: generalized Liouville–Caputo fractional derivative; ? -Laplace transformation; infinite time delay; mild solution; Leray–Schauder alternative (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (4)

Downloads: (external link)
https://www.mdpi.com/2227-7390/10/8/1332/pdf (application/pdf)
https://www.mdpi.com/2227-7390/10/8/1332/ (text/html)

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:gam:jmathe:v:10:y:2022:i:8:p:1332-:d:795815

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().