With the rapid advancement of sensor and network technology, there has been a notable increase in the availability of condition-monitoring data such as vibration, temperature, pressure, voltage, and other electrical and mechanical parameters. With the introduction of big data, it is possible to prevent potential failures and estimate the remaining useful life of the equipment by developing advanced mathematical models and artificial intelligence (AI) techniques. These approaches allow taking maintenance actions quickly and appropriately. In this scenario, this paper presents a systematic literature review of statistical inference approaches, stochastic methods, and AI techniques for predictive maintenance in the automotive sector. It provides a summary on these approaches, their main results, challenges, and opportunities, and it supports new research works for vehicle predictive maintenance.

The main purpose of this manuscript is to show asymptotic properties of a class of differential equations with variable coefficients ${\left(r\left(\nu \right){\left(w^{‴}\left(\nu \right)\right)}^{\beta }\right)}^{\prime }+{\sum }_{i=1}^j{q}_i\left(\nu \right)y^{\kappa }\left(g_i\left(\nu \right)\right)=0$ , where $\nu \ge {\nu }_0$ and $w\left(\nu \right):=y\left(\nu \right)+p\left(\nu \right)y\left(\sigma \left(\nu \right)\right)$ . By using integral averaging technique, we get conditions to ensure oscillation of solutions of this equation. The obtained results improve and generalize the earlier ones; finally an example is given to illustrate the criteria.

In this work, we consider a type of second-order functional differential equations and establish qualitative properties of their solutions. These new results complement and improve a number of results reported in the literature. Finally, we provide an example that illustrates our results.

The aim of this paper was to propose a systematic study of a $(1+1)$ -dimensional higher order nonlinear Schrödinger equation, arising in two different contexts regarding the biological science and the nonlinear optics. We performed a Lie symmetry analysis and here present exact solutions of the equation.