Fuzzy Mittag–Leffler–Hyers–Ulam–Rassias Stability of Stochastic Differential Equations

Reza Chaharpashlou, Reza Saadati and António M. Lopes ()
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Reza Chaharpashlou: Department of Mathematics, Jundi-Shapur University of Technology, Dezful 64615-334, Iran
Reza Saadati: School of Mathematics, Iran University of Science and Technology, Narmak, Tehran 13114-16846, Iran
António M. Lopes: LAETA/INEGI, Faculty of Engineering, University of Porto, Rua Dr. Roberto Frias, 4200-465 Porto, Portugal

Mathematics, 2023, vol. 11, issue 9, 1-11

Abstract: Stability is the most relevant property of dynamical systems. The stability of stochastic differential equations is a challenging and still open problem. In this article, using a fuzzy Mittag–Leffler function, we introduce a new fuzzy controller function to stabilize the stochastic differential equation (SDE) ν ′ ( γ , μ ) = F γ , μ , ν ( γ , μ ) . By adopting the fixed point technique, we are able to prove the fuzzy Mittag–Leffler–Hyers–Ulam–Rassias stability of the SDE.

Keywords: fuzzy Mittag–Leffler–Hyers–Ulam–Rassiass stability; fuzzy controller function; fuzzy normed space; random operator; stochastic differential equation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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