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This paper aims to study qualitative properties and approximate solutions of a thermostat dynamics system with three-point boundary value conditions involving a nonsingular kernel operator which is called Atangana-Baleanu-Caputo (ABC) derivative for the first time. The results of the existence and uniqueness of the solution for such a system are investigated with minimum hypotheses by employing Banach and Schauder's fixed point theorems. Furthermore, Ulam-Hyers (UH) stability, Ulam-Hyers-Rassias UHR stability and their generalizations are discussed by using some topics concerning the nonlinear functional analysis. An efficiency of Adomian decomposition method (ADM) is established in order to estimate approximate solutions of our problem and convergence theorem is proved. Finally, four examples are exhibited to illustrate the validity of the theoretical and numerical results.

This paper considered theoretical and numerical methodologies.

This paper contains the following findings: (1) Thermostat fractional dynamics system is studied under ABC operator. (2) Qualitative properties such as existence, uniqueness and Ulam–Hyers–Rassias stability are established by fixed point theorems and nonlinear analysis topics. (3) Approximate solution of the problem is investigated by Adomain decomposition method. (4) Convergence analysis of ADM is proved. (5) Examples are provided to illustrate theoretical and numerical results. (6) Numerical results are compared with exact solution in tables and figures.

The novelty and contributions of this paper is to use a nonsingular kernel operator for the first time in order to study the qualitative properties and approximate solution of a thermostat dynamics system.

In this paper, we consider a two color multi-drawing urn model. At each discrete time step, we draw uniformly at random a sample of m balls (m≥1) and note their color, they will be returned to the urn together with a random number of balls depending on the sample’s composition. The replacement rule is a 2 × 2 matrix depending on bounded discrete positive random variables. Using a stochastic approximation algorithm and martingales methods, we investigate the asymptotic behavior of the urn after many draws.

With the aid of naturalistic simulations, this paper aims to investigate human behavior during manual and autonomous driving modes in complex scenarios.

The simulation environment is established by integrating virtual reality interface with a micro-simulation model. In the simulation, the vehicle autonomy is developed by a framework that integrates artificial neural networks and genetic algorithms. Human-subject experiments are carried, and participants are asked to virtually sit in the developed autonomous vehicle (AV) that allows for both human driving and autopilot functions within a mixed traffic environment.

Not surprisingly, the inconsistency is identified between two driving modes, in which the AV’s driving maneuver causes the cognitive bias and makes participants feel unsafe. Even though only a shallow portion of the cases that the AV ended up with an accident during the testing stage, participants still frequently intervened during the AV operation. On a similar note, even though the statistical results reflect that the AV drives under perceived high-risk conditions, rarely an actual crash can happen. This suggests that the classic safety surrogate measurement, e.g. time-to-collision, may require adjustment for the mixed traffic flow.

Understanding the behavior of AVs and the behavioral difference between AVs and human drivers are important, where the developed platform is only the first effort to identify the critical scenarios where the AVs might fail to react.

This paper attempts to fill the existing research gap in preparing close-to-reality tools for AV experience and further understanding human behavior during high-level autonomous driving.

This work aims to systematically analyze the inconsistency in driving patterns between manual and autopilot modes in various driving scenarios (i.e. multiple scenes and various traffic conditions) to facilitate user acceptance of AV technology.

A close-to-reality tool for AV experience and AV-related behavioral study. A systematic analysis in relation to the inconsistency in driving patterns between manual and autonomous driving. A foundation for identifying the critical scenarios where the AVs might fail to react.