The thesis applies solutions to boundary value problems of a class of fractional differential equation coupled systems with a p-Laplacian operator. This article applies this part of the content to alleviate the psychological barriers of college students. This article transforms the tendency of individual consciousness in college students’ psychological counselling into a problem of solving boundary value problems of fractional differential equations. Studies have shown that using fractional differential equations to analyse the causes of college students’ psychological barriers has an essential role in eliminating college students’ psychological barriers.

#### Keywords

- Fractional differential equations
- psychological obstacles
- college students
- optimal solutions
- alternative terms
- consciousness
- transfer Intensity

#### MSC 2010

- 34K37

Psychological counselling is the process of changing the individual’s conscious tendency, which is a generally accepted view in clinical and counselling psychology. Freud’s psychoanalytic therapy, Rogers’s personal-centred therapy, Bandura’s behavioural therapy identified by Observation and Learning, Ellis’s rational emotion therapy, the reality therapy created by Glasser, and Pars’s Gestalt Therapy, Yang Guangxue’s narrative-hermeneutics theory, and empirical behaviour research are all based on theoretical assumptions about understanding human nature. Scholars’ research theories are derived from the techniques and methods of consultants’ philosophical attitudes. After they explored human psychology, they obtained a complete knowledge system [1]. This knowledge system develops their consultation and treatment techniques and applies them to practical consultation and treatment operations. Although various consultation theories and technologies have different understandings and operations of human nature, psychological consultation is still based on the interpersonal communication between the counsellor and the client. Of course, interpersonal communication is exceptional in the sense that it is different from ordinary communication.

From the consultant’s perspective, the consultant uses his or her professional background, theory, and knowledge system to develop the ability to explore psychological activities. The consultant and the client jointly face the problems faced by the client’s psychological world. It helps the person’s personality to improve, grow, and mature. From the perspective of the client, what the client has experienced is a process of changing consciousness. In this change process, the parties have to go through the process of their thinking activities [2]. Thought is the result of thinking activity. Thoughts and thoughts hide behind the language. Language can be used as a tool to observe the mental or thought activities caused by the person’s thinking activity.

This research follows the construction of consulting technology to process the consulting records from the clinic in a statistical sense. This article uses fractional differential equations to establish a model for alleviating the mental disorders of college students. At the same time, we use mathematical models to analyse the problem and make quantitative inferences about the possible flow of language terms in changing the consciousness of the parties in psychological counselling [3]. We examine the possible degree of change in the linguistic terms of the party’s conscious tendency through analysis.

(1) The language process is the material carrier of the thinking process, it expresses the tendency of consciousness. The consultant can convert the spoken language of the client into a written language. (2) The terms and concepts in the language expressions of the parties have the same relationship. (3) Consciousness orientation can be expressed in the form of definition. Defined in language expressions is a combination of terms that state the nature of a sentence and propositional expressions. (4) The consultant abandons the expression of specific incidents and emotional vents of the parties concerned. The consultant only pays attention to transforming the spoken language about the conscious tendency into a written language. (5) The consultant uses lexical questions to intervene in changing the parties’ consciousness. (6) The counsellor regards the psychological process of the client as the objective object of the consultation process. The consultant can ignore factors such as the person’s gender, age and region.

(1) The number of conversions is got when the person’s spoken language is converted into written language. (2) The number of vocabulary items is the sum of the number of language expression vocabularies. This includes the number of subject terms, predicate terms and object terms. (3) The term being attacked means that the party accepts the question of the term from the consultant. A particular term is selected as the transfer point of the party’s consciousness.

Consultation target standards: When the consultation contract is terminated, if the party’s expression of consciousness tendencies and the expression of the consultation contract at the time of the establishment of the consultation contract change in content and cognitive perspective, it is deemed that the consultation goal has been achieved.

The function of consultation: After the vocabulary is attacked, the party is at the point of shifting consciousness [4]. The vocabulary has been attacked many times to strengthen the direction of the shift of consciousness.

The work performance of the consultant: The consultant has been professionally trained and has the quality of consulting to preside over and complete the consulting activities.

Considering the strength of the client’s conscious tendency, the intensity of the client’s consciousness transfer from receiving counselling is three times the intensity of the consciousness transfer from the self.

The calculation of the model is based on the Means mean and standard deviation from the statistical processing data of clinical consultation records.

_{i}_{i}_{ni}_{x}_{n}_{s}_{x}

We use differential equations to establish mathematical models. Under the premise of achieving a certain consulting target expectation degree

The

The

Given

Then we call it the

The

For any

For any _{0}

For any

For any _{0}_{0} = max{^{2}}; ^{a−}^{2}(1 ^{2}; ^{2}(1 ^{a−2}.

We assume that X is a real normed linear space. Ω_{1}, Ω_{2} ⊂ _{2} →

∀_{1}, ǁ_{2}, ǁ

∀_{1}, ǁ_{2}, ǁ

We assume that the intensity of consciousness transfer before the client has not received the consultation is

The intensity after the previous alternative is attacked obtained for the same reason as the above formula:
_{x}_{x}_{x}_{s}_{x}_{s}_{x}/dV_{x}_{x}_{X}_{x}_{2} into
_{s}_{x}_{s}_{x}

Here we need to determine parameter _{x}_{x}_{x}_{x}_{x}_{x}_{x}_{min} = 2. We will take [_{x}_{max} = 5 after the consultation. In the model’s hypothesis, we take into account the fixation of the vocabulary, the intensity of the consciousness transfer of the party is equal to the intensity of the consciousness parties’ conscious tendencies. Figure 2 shows the relationship between the optional amount of psychological counselling terms and the intensity of self-consciousness transfer. The intensity of the consciousness transfer of the client from receiving counselling is three times the intensity of consciousness transfer from the self. We can establish functional relationships:

When _{x}_{x}_{min} = 2; When _{x}_{x}_{min} = 5 and the function is incremented. The parameter _{x}_{x}

This research aims to use mathematical language to describe the possible process of changes in the parties’ consciousness. Language is the material carrier of thinking and mental activity. Its estimation of the flow of terms that make up the language can be used as a perspective to observe the psychological activities of people hidden behind the language. From the derivation process of the differential equation model, we can see the change process of the intensity of consciousness transfer after the party accepts the attack of the progressive term. Moreover, the party’s self-consciousness transfer intensity will increase after receiving the attack and intervention of the terms derived from the consultation [11]. The proportional function _{x}_{s}

In this research, it is assumed that in any consulting operation under consulting theory, the consultant can obtain the number of alternative terms that can provide the term attacked by the number of conversions from spoken language to written language. The simulation of the mathematical model of the consultation process in this study can also show that the acquisition of the lexical item alternative is also the consultant finding a way to enter the client’s psychological state [12]. The flow of alternative terms indicates the sportiness of the person’s mental activity. With this, the consultant can observe the point-and-face performance, depth source, and possible trend of the party’s conscious tendencies. This can also observe and find an opportunity to change the conscious tendency of the parties.

This research model’s progressive term attacked alternative flow calculation scheme applies to every consultation operation under the consultation background hypothesised in this research. By calculating the optional quantity of terms, the workability of the consultant can be distinguished from the ability of the client’s personality to self-improvement. The establishment of the model can help the counsellor better observe the changes in the client’s psychological activities during the consultation. When appropriate, this can support the client, which may be conducive to the improvement, growth, and maturity of the client’s personality. The significance of establishing this model is to describe how the change of the subject’s alternative flow of terms during the consultation process may cause a change in consciousness. Therefore, the measurement results of the specific quantitative values of the model do not become an argument to prove the superiority of the model. However, the calculation of the intensity of the transfer of the party’s self-consciousness relative to the enhancement rate of the attacked terms derived from the consultation is the key to the model’s effectiveness. The _{x}/dV_{x}

The article quantifies the index data through consulting on-site records to make statistics and sorting out the data. We give a consistent estimate of the exogenous parameters in the model to accurately measure the scale. We need to further optimise the model by accurately quantifying the ratio between the intensity of the impact of the term being attacked and the intensity of the person’s self-conscious transfer.

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