Qualitative Analysis of Fractional Stochastic Differential Equations with Variable Order Fractional Derivative

This research paper has been dedicated to the investigation of Coupled System of Fractional Stochastic Differential Equations (CSFSDEs), which is an extension of Fractional Stochastic Differential equations, an emerging field that is in a developmental stage and demands the focused attention of experts. Within this context, the research article is mainly focused on determining solutions for CSFSDEs featuring variable order derivatives. This article will lay the foundation for establishing the necessary conditions for the existence and uniqueness of the considered CSFSDEs. To achieve this, we have employed Picard’s iteration techniques, which have proven effective in this domain. Furthermore, we will set the groundwork for defining conditions of Ulam’s type stabilities specific to the proposed model. To conclude this work, we have presented an illustrative example that serves to explain the primary findings of our research.