Cardiovascular diseases (CVDs) remain the leading cause of death worldwide. Patients at risk of evolving CVDs are assessed by evaluating a risk factor-based score that incorporates different bio-markers ranging from age and sex to arterial stiffness (AS). AS depicts the rigidity of the arterial vessels and leads to an increase in the arterial pulse pressure, affecting the heart and vascular physiology. These facts have encouraged researchers to propose surrogate markers of cardiovascular risks and develop simple and non-invasive models to better understand cardiovascular system operations. This work thus fundamentally capitalizes on developing a novel class of low-dimensional physics-based fractional-order models of systemic arteries and exploring the feasibility of fractional differentiation order to portray the vascular stiffness. Fractional-order modeling is a successful paradigm to integrate multiscale and interconnected mechanisms of the complex arterial system. However, this type of modeling alone often fails to efficiently integrate altered variabilities in vascular physiology from various sources of large datasets, multi-modalities, and levels. In this regard, combining fractional-order-based approaches with machine learning techniques presents a unique opportunity to develop a powerful prediction framework that reveals the correlation between intertwined vascular events. This work is divided into three parts. The first part contributes to developing the fractional-order lumped parametric model of the arterial system. First, we propose fractional-order representations to model and characterize the complex and frequency-dependent apparent arterial compliance. Second, we propose fractional-order arterial Windkessel modeling the aortic input impedance and hemodynamic. Subsequently, the proposed models have been applied and validated using both human in-silico healthy datasets and real vascular aging and hypertension. The second part addresses the non-zero initial value problem for fractional differential equations (FDEs) and proposes an estimation technique for joint estimation of the input, parameters, and fractional differentiation order of non-commensurate FDEs. The performance of the proposed estimation techniques is illustrated on arterial and neurovascular hemodynamic response models. The third part explores the feasibility of using machine learning algorithms to estimate the gold-standard measurement of AS, carotid-to-femoral pulse wave velocity. Different modalities have been investigated to generate informative input features and reduce the dimensionality of the time series pulse waves.

This work revolves around the use of fractional order calculus in control science. Techniques such as fractional order universal adaptive stabilization (FO-UAS), and the fascinating results of their application to real-world systems, are presented initially. A major portion of this work deals with fractional order modeling and control of real-life systems like heat flow, fan and plate, and coupled tank systems. The fractional order models and controllers are not only simulated, they are also emulated using analog hardware. The main aim of all the above experimentation is to develop a fractional order controller for plasma position control of the Saskatchewan torus-1, modified (STOR-1M) tokamak at the Utah State University (USU) campus. A new method for plasma position estimation has been formulated. The results of hardware emulation of plasma position and its control are also presented. This work performs a small scale test measuring controller performance, so that it serves as a platform for future research efforts leading to real-life implementation of a plasma position controller for the tokamak.