Their psychology largely influences the behavior of higher vocational students. The various forms of psychology determine the diversity of students' behavior in higher vocational colleges. The behavior of higher vocational students is not only affected by subjective factors such as their psychological cognition level but also by objective factors such as changes in society, school, and family environment [1]. Therefore, improving the health quality of higher vocational students has become the main problem to be solved urgently in the current ideological and political education work in colleges and universities. This has also become the focus of research by relevant experts and scholars in ideological education. Some scholars have proposed an optimization modeling method of higher vocational students' mental health quality based on granularity transformation. Some scholars have proposed an optimization modeling method for the mental health quality of higher vocational students based on the introduction of characteristic tendencies. Based on kernel clustering, some scholars have proposed an optimization modeling method of higher vocational students' mental health quality [2]. These traditional methods generally have the problems of low modeling accuracy, complicated modeling process, and long time-consuming. Therefore, we propose an optimal modeling method for higher vocational students' mental health quality based on fractional differential equations.

In establishing the principle model of the higher vocational students' psychological information system, we first obtain the outstanding psychological and physiological characteristics of the higher vocational students. Through this feature, we analyze the objective factors of the external environment and the main factors of the higher vocational students' psychological production [3]. At the same time, the paper builds the principle model of the higher vocational students' psychological information system. The specific steps are detailed as follows:

_{1}, _{2}, ⋯, _{i}_{1}, _{2}, ⋯, _{i}_{1}, _{2}, ⋯, _{i}

We use the principle model of higher vocational students' psychological information system to optimize the modeling of mental health quality. At this point, we should analyze the relationship between psychology and behavioral barriers in great detail. But the traditional method is to introduce a mapping table and a threshold for the misclassification rate [6]. We need to complete the modeling according to the attributes of different mental health quality categories. However, this method is difficult to extract the characteristics of vocational students' psychological phenomena accurately. At the same time, this method has the problem of large modeling errors. Therefore, we propose an optimal modeling method for higher vocational students' mental health quality based on fractional differential equations.

We obtained the essence of higher vocational students' psychology in modeling the effect of higher vocational students' rebellious psychology on behavioral hindrance [7]. At the same time, we give different stages of rebellious psychology of higher vocational students. At this time, the corresponding information entropy of the behavioral hindrance generated by each stage of the rebellious psychology of higher vocational students is obtained. We calculated the threshold of the behavioral tendency of higher vocational students to produce rebellious psychology. The specific process is as follows:

{_{1}, _{2},⋯, _{k}_{i}_{i}_{i}

We obtained the set of subjective and objective factors of higher vocational students' formation of rebellious psychology in modeling the effect of higher vocational students' rebellious psychology on behavioral hindrance [11]. At the same time, we give the objective function of the relationship between the rebellious psychology of higher vocational students and their behavioral obstacles. A problem model of the effect of rebellious psychology on the behavioral hindrance of higher vocational students is established. The set of all factors that set the behavior tendency dominated by the rebellious psychology of higher vocational students is expressed as follows
_{k}_{k}_{ik}_{k}_{i}_{k}_{i}

We set up a model of higher vocational students' psychological hindrance to behavior. At the same time, the article is based on the problem model of higher vocational students' rebellious psychology on behavioral hindrance. We use ant theory to solve the problem model. At this time, we effectively set up an optimization model for the mental health quality of higher vocational students. The specific process is as follows:

_{ij}_{ij, k} represents the pheromone that ant _{k}_{ij}_{ij}_{ij}_{ij, k}_{ij, k}_{ij}_{j}_{ij}_{i}_{j}_{j}_{j}_{ij}_{ij}_{ij}

When a person is relaxed, alertness _{t}_{t}_{t}_{t}_{t}_{Q}_{Q}_{t}_{0}

_{1}, _{2} in vigilance potential rhythm, amplitude _{1}_{2}_{a}_{Q}_{w}

We prove the comprehensive validity of the optimization model of mental health quality of vocational students based on fractional differential equations. At this point we need to experiment. This article builds a modeling simulation platform for higher vocational students' mental health quality under the environment of Matlab. We use questionnaires to conduct statistics. At the same time, the survey results are divided into 5 sample sets and 5 test sets. We use the model of this paper and the model of literature and literature to carry out statistical experiments on the optimization of the mental health quality of vocational students. We compare the three models' statistical efficiency (%) (Figure 1).

The statistical efficiency of using the model in this paper to optimize the mental health quality of higher vocational students is higher than that of the literature and literature models. We use the model of this paper and the model of literature and literature to conduct statistical experiments on the effect of higher vocational students' psychology on behavioral hindrance. The statistical stability (%) of the effect of college psychology on behavioral hindrance was compared among the three models (Figure 2).

We use the model in this paper to calculate the statistical stability of higher vocational students' psychological hindrance to behavior, which is better than the literature and literature models. We use the model of this paper, and the model of literature and literature carry out statistical experiments on the optimization of the mental health quality of vocational students. We compare the three models to compare the statistical time complexity (%) of higher vocational students' mental health quality optimization modeling (Figure 3).

We use the model in this paper to optimize the mental health quality of higher vocational students. The statistical time complexity is lower than the literature and literature models.

This paper proposes an optimal modeling method for mental health higher vocational students based on fractional differential equations. The simulation results show that the proposed model has great advantages in modeling efficiency, stability, and time complexity. This provides a strong basis for improving the mental health of vocational students.

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