Chapter 410 (1/2)
Chapter 413
any integral and derivative of real or complex order is usually called fractional derivative. Fractional calculus is widely used in viscoelastic mechanics, statistical and stochastic processes, dynamic system control and optical signal processing, and has rich theoretical connotation.
In this paper, we use the theory of continuous functions and Banach contractive mapping to study the existence of boundary value solutions for Nonlinear Differential Equations with fractional derivatives.
Do not need to do too deep understanding, Cheng Nuo only need to know a general, can calmly deal with any problem.
Cheng Nuo turned back page after page without haste. Although Cheng didn't deliberately speed up his speed, he seemed to have seen a ghost in the eyes of the three members of the same group.
He, is this really serious, not perfunctory us?
Thinking like this, the boy's eyes again fell on the Chali students, full of sorrow. It means, ”this out of tune guy is your boy who invited him here?”
Once again, zari wanted to cry without tears.
As time goes by, more than ten minutes later, Cheng put the pile of A4 paper in his hand back on the desktop and said with a smile, ”I just read your research content from the beginning to the end. If I guess well, you should be in trouble at the end of the differential equation boundary value analysis based on Banach compressed image?”
The three eyes fell on the students in Chali.
Why me again?!
”Don't look at me. I just told the God to ask him to help. I didn't say the specific problems we met. If you do not believe, ask the great God
Cheng Nuo took a few blank drafts from one side of the table and said, ”zari really didn't mention the specific content to me. However, it is not difficult to guess that your research report, in the final boundary value analysis part, lacks a large part of the proof process. I think it should not be deliberately missed. ”
The boy nodded, which was recognized by Cheng Nuo, ”indeed, in this part, although we know what the desired result is, we have thought about the specific process for several days, but we have not come up with a result.”
Just Cheng Nuo's performance has made the boys' impression of Cheng Nuo better.
This student, it seems, is not so common!
So he asked tentatively, ”since you know the trouble we are in, is there any way to solve it?”
Cheng Nuo smile, erect a finger, swing, slowly spit out two words, ”not difficult!”
Chali's face was happy.
The boy rocky took a puff from the corner of his mouth.
Why do I have the feeling of watching the live broadcast of ”force king”?
Rocky, the truth, is waiting for Cheng Nuo to speak.
”I think a large part of the reason why you have been writing on this issue for such a long time is due to the wrong method.”
”In the wrong way?”
”Yes Cheng Nuo tapped the table top with his pen cap. ”Let me ask you a question first. What is the nonlinear differential equation of fractional derivative?”
The boy subconsciously replied, ”the nonlinear differential equation of fractional derivative can be summarized by two formulas: F-1 (z) + (D + DT) (z) - f (x, (z)), Z ∈ (0, 1), and Y (0) = 0 = y (1).”
Cheng Nuo nodded with satisfaction, ”that's right. But do you remember the fractional derivative and the conditions for its existence? ”
Existence condition? Rocky was stunned.