@mmcdara 

alpha>0, 
beta>0 
and 1>alpha+beta>0

and we suppose mu>1 

I tried also asymp  to get the asymptotic of F when t goes to infinity but unfortunately no result obtained

@acer 

I appreciate your comments

@Rouben Rostamian  

Thank you for your code. I really appreciate the result to verify my computation by hand. 
By, when I run the code, I obtain the following erros, I don't understand the kind of these errors.

Thank you

@tomleslie 

curve_three_d.mw

@Carl Love 

Thank you for your help

The modification proposed are added in the code,

But its seems that the x axis is used in the reverse order,

The  x-axis from 1740 to 4033 , but the figure show that the x-axis is  reversed,

@Carl Love 

Thank you

@tomleslie 

Thank you for your answer

@tomleslie 

My problem is solved based on your code 

thank you

@acer 

Thank you

 I appreciate your remarks

@tomleslie 

@tomleslie
According to all remarks received, I tried to do my best to correct the code.  

code1.mw

But wht the code does not add blocks of matrix K, 

This code, is exactly similar to matlab code presented in the following link, used to solve odes by finite element

https://www.youtube.com/watch?v=l4Y3iQrPBa8

thank you for all remarks 

@acer 

thank you for your remark

@acer 

compare other method with fsolve

@Carl Love 

Thank you for your code, 
can we can add a table that display the value of x and y  during iterations, so that I can change the initial guess and  compare the iterations needed to converge to the minimum. 

@vv 

If sin(n)<0, the sequence becomes 
an:=(n + sqrt (n(n+7))+9)^n
using Cauchy criteria 

an^1/n=(n + sqrt (n(n+7))+9) --->infinity, and thus R=0,  BUT you propose 2/25..... HOW dit you get this limit