Joint models can be used to study a longitudinal biomarker process, the effect of covariates on the biomarker process, the effect of covariates, and the biomarker process on the terminal/recurrent event process. Many studies have used the random-effects model to study the biomarker progress over time. However, the high variability arising from biological processes cannot be effectively explained by using a simple random-effects model. Our novel approach uses a linear mixed-effects model with an integrated fractional Brownian motion (IFBM) process to capture within-subject variation, and allowing the model to follow a multivariate Normal distribution. We use a Cox proportional hazards model for the survival sub-model. The two sub-models are joined through a shared parameter, which depicts the association of the biomarker process with the event process. Bayesian methods are used to fit the model. We perform a simulation study of our joint model with scaled integrated Brownian motion and a joint model without a stochastic process.