On Caputo–Katugampola Fractional Stochastic Differential Equation

McSylvester Ejighikeme Omaba and Hamdan Al Sulaimani
Additional contact information
McSylvester Ejighikeme Omaba: Department of Mathematics, College of Science, University of Hafr Al Batin, P.O. Box 1803, Hafr Al Batin 31991, Saudi Arabia
Hamdan Al Sulaimani: Department of Mathematics, College of Science, University of Hafr Al Batin, P.O. Box 1803, Hafr Al Batin 31991, Saudi Arabia

Mathematics, 2022, vol. 10, issue 12, 1-12

Abstract: We consider the following stochastic fractional differential equation C D 0 + α , ρ φ ( t ) = κ ϑ ( t , φ ( t ) ) w ˙ ( t ) , 0 < t ≤ T , where φ ( 0 ) = φ 0 is the initial function, C D 0 + α , ρ is the Caputo–Katugampola fractional differential operator of orders 0 < α ≤ 1 , ρ > 0 , the function ϑ : [ 0 , T ] × R → R is Lipschitz continuous on the second variable, w ˙ ( t ) denotes the generalized derivative of the Wiener process w ( t ) and κ > 0 represents the noise level. The main result of the paper focuses on the energy growth bound and the asymptotic behaviour of the random solution. Furthermore, we employ Banach fixed point theorem to establish the existence and uniqueness result of the mild solution.

Keywords: asymptotic behaviour; Caputo–Katugampola; Caputo–Hadamard; energy-growth bounds; well-posedness (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 (1)

Downloads: (external link)
https://www.mdpi.com/2227-7390/10/12/2086/pdf (application/pdf)
https://www.mdpi.com/2227-7390/10/12/2086/ (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:12:p:2086-:d:840206

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 ().