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.
Highlights
This work is concerned with the existence and uniqueness of solutions to the following problem of k-dimensional nonlinear fractional stochastic differential equations with variable order (VOFSDEs)
We introduce a new class of Caputo-type nonlinear VOFSDEs
We have defined an iteration sequence involving variable fractional order, which converges to the unique solution of the main problem
Summary
This work is concerned with the existence and uniqueness of solutions to the following problem of k-dimensional nonlinear fractional stochastic differential equations with variable order (VOFSDEs).
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