Omnipotent Data

Chapter 413

Any real or complex integral and derivative are usually called fractional calculus. Fractional calculus has applications in viscoelastic mechanics, statistics and stochastic processes, dynamic system control, and optical signal processing. Theoretical connotation.

Chali and his group are using continuous functions and Banah compression mapping theory to study the problem of the existence of solutions for the boundary value of nonlinear differential equations with fractional derivatives.

There is no need to do too much in-depth understanding, Cheng Nuo only needs to know a general outline, and he can deal with any problem calmly.

Cheng Nuo turned the pages in a hurry. Although Cheng Nuo did not deliberately speed up, in the eyes of the three members of the research team in Chali, it was like seeing a ghost.

He, is this really taking a serious look, not just playing us?

Thinking this way, the boy's eyes fell on Classmate Chali again, full of pity. It means, "This inconspicuous fellow was invited by your kid?"

Chari wanted to cry again without tears.

Time passed by, ten minutes later, Cheng Nuo put the stack of A4 papers in his hand back on the desktop and smiled, "I just read your research from beginning to end, if I guessed right. If yes, you should have trouble with the boundary value analysis of the differential equation based on the Banah compressed image at the end, right?"

The three of them all cast their eyes on Classmate Chali.

Why is it me again? !

Chali rolled his eyes and said silently, "Don't look at me, I just told the great **** to ask him for a favor, and didn't say the specific problem we encountered. If you don't believe it, ask the great god?"

Cheng Nuo took a few blank draft papers from one side of the table, and said, "Cali did not mention the specific content to me. But it is not difficult to guess that your research report is in the final margin. Analyzing that part, a large part of the proof process was missing. I think it was not deliberately omitted."

The boy nodded, as Cheng Nuo recognized, "Indeed, in this part, although we know what the desired result is, but the specific process, several of us have thought about it for several days, but we haven't gotten any results. ."

Cheng Nuo's performance just now has changed the boys' impression of Cheng Nuo.

This schoolboy does not seem so unusual!

So he asked tentatively, "Since you know the trouble we are having, is there a way to solve it?"

Cheng Nuo smiled, put a finger up, and slowly spit out two words, "Not difficult!"

Classmate Chali looked happy.

The boy Rocky's mouth twitched.

Why do I have a feeling of watching the live broadcast of the king?

Rocky, who had learned the truth, waited for Cheng Nuo to speak.

"I think that a large part of the reason why you have been inking on this issue for so long is because you used the wrong method."

"Wrong method?"

"Yes!" Cheng Nuo tapped the desktop with his pen cap, "Let me ask you a question first, what is a nonlinear differential equation with a fractional derivative?"

The boy subconsciously answered, "The nonlinear differential equation of the fractional derivative can be summarized by two formulas: f-(z)+(D+Dt)(z)-f(x,(z)), z∈( 0, 1), and y(0)=0=y(1)."

Cheng Nuo nodded very satisfied, "That's right. But do you still remember this fractional derivative and its existence conditions?"

Existence conditions? Rocky was taken aback.

Cheng Nuo explained, “With a certain Dirihlet boundary value, there will be such an existence condition for differential equations of order derivatives.”

Cheng Nuo picked up the pen and wrote on the paper, D0+y)(x)=(D1-y)(x), (D1-y)(x)=(D-y)(x)."

Looking at the formula written by Cheng Nuo, the boy fell into deep thought.

But Cheng Nuo did not give him time to think. He is not a teacher of a few people, there is no need to follow their rhythm.

He went on to elaborate on his own point of view, "You are trying to prove that there is a unique solution to the boundary value of the fractional derivative nonlinear differential equation. The method is to directly derive the formula and use the Banah compressed image theory to get the result."

"But based on the two existence conditions I wrote just now, this method is 100% wrong!" Cheng Nuo said confidently.

"That..." the boy couldn't help but speak.

Cheng Nuo pressed his hands down and said with a smile, "Students, don't be so anxious. Keep your aura and aura smooth. I'll talk about the correct way to prove it right away."

Cheng Nuo first wrote three keywords on the draft paper: Green function, Lipshitz compression condition, Banah space.

"My method of proof is very simple. In fact, as long as you understand my three key words, it is only a matter of time before you understand. However, in order to save the time for both parties, I will derive it directly." Cheng Nuo's tone is very flat and rational The ideas in my mind are like lectures, writing while talking.

"The first step is to use the perturbation method combined with the Green function to further study the boundary value problem of differential equations with left and right fractional derivatives, and give a Dirihlet boundary value problem for homogeneous differential equations, then u(x)=0, x∈( 0,1), y(0)=0=y(1)."

"Assuming that the function f(x, u) is continuous on [0,1[×(+∞,-∞)-(一oo,+oo), the homogeneous boundary value problem can be described as -u\'\ '(x)=f(x, u(x)), x∈(0,1), u(0)=0=u(1). where u(x) represents the solution of the boundary value problem."

…………

"...Through the above theorem, it can be obtained that the boundary value problem has a unique solution on the continuous function space C[O,1]. From the known conditions, we know that in the continuous space C[O,1], the operator T satisfies the Lipshitz compression Condition, according to the Banah compressed image theory, the operator T has a unique fixed point Y ∈ [o, 1] in space, which conforms to..."

"... Through the above definition and theorem, it can be proved that there is a unique solution for the boundary value of the fractional derivative nonlinear differential equation!"

While talking and writing, Cheng Nuo spent nearly twenty minutes to deduce the problem of proving that the boundary value is the only solution to the Chali four from beginning to end.

Except for Chali, who has already developed immunity, the other three are in a state of brain crash.

This is... over? !

At the beginning, the four of them had been studying for two days and two nights~www.readwn.com~ and they didn't find out why.

But when it came to Cheng Nuo, how could it be twenty minutes?

Is this the gap between genius and mediocrity? But it's too realistic, right?

Mickey looked at him with a bitter expression, staring at Cheng Nuo, who was sitting on the chair with a calm expression, with mixed feelings in his heart.

Look at it! You got slapped!

He did not expect that the legendary wizard that was rare in a century would really be met by him!

He walked to Chali and asked bitterly, "Chali, what is your friend's name? Why have I never heard of this person in our college?"

Chali shrugged, "It's normal that you haven't heard of it, because the great **** is no longer interested in making things happen in the school. You know the Cheng Nuo theorem that has become popular recently, it was the great **** proposed!"

hiss!

Mickey is horrified but shocked!