To systematically understand the ability and technical mastery of football training of ethnic college students in colleges and universities, we use fractional differential equations to analyze the passing technique of college ethnic football. Research has found that establishing differential equation models in football can help us use mathematical ideas, methods, and knowledge to solve practical problems.

#### Keywords

- fractional differential equations
- colleges and universities
- physical training
- generalized path
- line graph analysis
- transfer coordination

#### MSC 2010

- 35A24

In sports training in colleges and universities, people generally equate a team's offensive ability with the striker's level of ‘one-to-one’ [1]. In the fierce competition in football, the forward is an essential factor in winning, but the passing and receiving cooperation from the backcourt and midfielders is also essential.

Network topology has been widely used in communication networks, computer networks, and operations research. Here we use line graph analysis in network theory to discuss passing and receiving in football [2]. We first define the generalized path
_{i}_{i}_{jk}_{m×l}, _{jk}_{l×n},

For example, ^{T},

We use Figure 1 to show the generalized path diagram of the pass when attacking. _{1} represents the node formed by the defender of the possession side and the goalkeeper. _{2}, _{3} corresponds to midfielders and full-backs. _{4} stands for striker. _{5} refers to the goal. Then

The same
_{j}_{k}_{j}_{k}_{1}, _{5} is constant for the stadium. The value of
_{2}, _{3}.

The best-generalized path gives us the whereabouts of the ball in the pass. But how to form the best path is primarily affected by the defensive team's defensive lineup. Let us illustrate this point with a simple diagram [4]. The three _{1}, _{2}, _{3} secant lines in Figure 2 below represent the three defense lines of the defender. And define

We introduce the concept of generalized attack intensity and define the following formula. The attack intensity in football refers to the attack intensity, the reliability of passing and receiving the ball, and the degree of threat to the defense [5].

A linear model can represent the generalized attack intensity secant

The minimum cut is equivalent to the maximum flow, so the generalized attack intensity cut is
_{5}. This is the value that forms the minimum secant _{3} to form the maximum attack intensity [6].

We can write the dynamic equations of the model by the Kane method

We replace the extra force acting on the system with an equal force system. Then the generalized active force _{j}_{k}_{k}_{k}_{k}_{k} ·V_{k}_{k}_{k}_{k}_{k}_{k}_{l}_{k}_{l}_{k}

Due to

Equation (17) can be rewritten as
_{ki}_{k}_{oi}

Among them

The inertial dyadic _{k}

Among them, the value of element _{mnk}_{om}_{mnk}_{kr}_{ks}

Organized

Among them
_{jp}_{j}

Equation (24) forms 40 second-order nonlinear differential equations. Use the Runge-Kutta method to find numerical solutions to these equations. We can find 40 generalized coordinates. If some equations of these generalized coordinates are known, a part of the Eq. (24) becomes an algebraic equation for finding the sum of unknown forces [9]. All the coefficients in the equation can be obtained by calculating the four coefficient matrices of _{ijk}_{ijk}

To obtain the dynamic equation of the constraint system, we only need to multiply the left side of the dynamic equation of the original system by transposing the coefficient matrix of the constraint equation [10]. Therefore, from Eq. (24), the dynamic equation of the multi-rigid body mechanical model of the human body under constraints can be obtained:
_{jp}_{j}

The election here is one of the ten classic World Cup events-a-goal matches between Argentina and the Netherlands. The picture is the eight sports characteristic pictures from the attack from the middle of the ball to the goal. Through image reconstruction, a panoramic view of the whole process is obtained [11]. From the reconstructed panorama, the combination line of passing and receiving for the offensive midfielder is obtained as shown in Figure 3:

According to the offensive strength, the offensive midfielder's adequate passing directions, namely, to the right and pass back. The defense of the three forwards on the offensive side is successful for the defense. Still, the defensive guards are too densely positioned to create opportunities for the proper offensive back [12]. Although a ‘6-3 situation is formed in the local area, there is unnecessary defensive overlap, resulting in insufficient defensive space. At this time, the three strikers of the offensive side are effectively blocked, and the goalkeeper's proper position is not a fatal threat to the defensive side.

Figures 4 and 5 are the characteristic pictures of the ‘back bow’ on the pole in the shooting action using the improved dynamic model and the original model [13]. It can be seen that the hip movement, which is the crucial part of the technical movement, more realistically describes the characteristics of the movement by increasing the degree of freedom.

The essential physical fitness and technical level of a football player are essential. It is an integral part of the technical level of the entire team. However, the most considerable charm of football is the ‘acting’ of talented players and the unpredictable results. The team's tactical style and performance are also the most attractive. Research has found that establishing differential equation models in football can help us use mathematical ideas, methods, and knowledge to solve practical problems.

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