On the Existence and Uniqueness of Solutions for Multidimensional Fractional Stochastic Differential Equations with Variable Order

Seyfeddine Moualkia and Yong Xu
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Seyfeddine Moualkia: School of Mathematics and Statistics, Northwestern Polytechnical University, Xi’an 710072, China
Yong Xu: School of Mathematics and Statistics, Northwestern Polytechnical University, Xi’an 710072, China

Mathematics, 2021, vol. 9, issue 17, 1-12

Abstract: Fractional stochastic differential equations are still in their infancy. Based on some existing results, the main difficulties here are how to deal with those equations if the fractional order is varying with time and how to confirm the existence of their solutions in this case. This paper is about the existence and uniqueness of solutions to the fractional stochastic differential equations with variable order. We prove the existence by using the Picard iterations and propose new sufficient conditions for the uniqueness.

Keywords: fractional stochastic differential equations; variable order; existence and uniqueness (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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