Numerical Approximation for a Stochastic Caputo Fractional Differential Equation with Multiplicative Noise

James Hoult and Yubin Yan ()
Additional contact information
James Hoult: School of Computer and Engineering Sciences, University of Chester, Chester CH1 4BJ, UK
Yubin Yan: School of Computer and Engineering Sciences, University of Chester, Chester CH1 4BJ, UK

Mathematics, 2025, vol. 13, issue 17, 1-23

Abstract: We investigate a numerical method for approximating stochastic Caputo fractional differential equations driven by multiplicative noise. The nonlinear functions f and g are assumed to satisfy the global Lipschitz conditions as well as the linear growth conditions. The noise is approximated by a piecewise constant function, yielding a regularized stochastic fractional differential equation. We prove that the error between the exact solution and the solution of the regularized equation converges in the L 2 ( ( 0 , T ) × Ω ) norm with an order of O ( Δ t α − 1 / 2 ) , where α ∈ ( 1 / 2 , 1 ] is the order of the Caputo fractional derivative, and Δ t is the time step size. Numerical experiments are provided to confirm that the simulation results are consistent with the theoretical convergence order.

Keywords: stochastic Caputo fractional differential equations; stability; Brownian motion (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/13/17/2835/pdf (application/pdf)
https://www.mdpi.com/2227-7390/13/17/2835/ (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:13:y:2025:i:17:p:2835-:d:1740920

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 ().