Existence Results for Langevin Equation Involving Atangana-Baleanu Fractional Operators

Dumitru Baleanu, Rahmat Darzi and Bahram Agheli
Additional contact information
Dumitru Baleanu: Department of Mathematics, Cankaya University, 06790 Ankara, Turkey
Rahmat Darzi: Department of Mathematics, Neka Branch, Islamic Azad University, Neka, Iran
Bahram Agheli: Department of Mathematics, Qaemshahr Branch, Islamic Azad University, Qaemshahr, Iran

Mathematics, 2020, vol. 8, issue 3, 1-12

Abstract: A new form of nonlinear Langevin equation (NLE), featuring two derivatives of non-integer orders, is studied in this research. An existence conclusion due to the nonlinear alternative of Leray-Schauder type (LSN) for the solution is offered first and, following that, the uniqueness of solution using Banach contraction principle (BCP) is demonstrated. Eventually, the derivatives of non-integer orders are elaborated in Atangana-Baleanu sense.

Keywords: Atangana-Baleanu fractional derivative; Langevin equation; Leray-Schauder nonlinear; existence results (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/8/3/408/pdf (application/pdf)
https://www.mdpi.com/2227-7390/8/3/408/ (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:8:y:2020:i:3:p:408-:d:331853

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 ().