How to implement this function using Matlab.

Hi I need to implement this function using matlab, where x and t are variables.

Please tell me how to do this.

[John BG]

Hi Kintali Narendra

this is John BG <mailto:[e-mail] [e-mail]>

if f(x) one or more asymptotic points within interval [0 x], the integral may not solve; can we assume that f(t) does not have any discontinuity within [0 x], both x and 0 included?

[John BG]

Also, you have to constrain f(t) to for instance polynomials with at least the term (x-t)^b, b>alpha, b<-alpha-2 or f(t) exponential that within [0 x] allows 1/(x-t)^alpha to be integrated, can some of these conditions be applied?

[David Goodmanson]

Hi kintali,

see

https://pdfs.semanticscholar.org/0df4/82a71f47d9fa6be27def92ef93873eb27a85.pdf

[Bastien Rouzé]

You could use a discrete scheme first (for the d/dx firstly, then for the sum) with a constant step and try to compute it. From this, you may be able to perform the complete calculus.

[kintali narendra]

Thank you John,David and Bastien, The paper which David referred has the solution. John I didn't understand your question.

[John BG]

Hi Kintali Narendra

this is John BG <mailto:[e-mail] [e-mail]>

I was just highlighting the point that certain constraints should be applied to f(t) before attempting the definition of D, otherwise it might happen that the integral cannot be solved, integral for instance Inf, and then D couldn't be defined.

Thanks for letting us know that you have already found the solution.

I hope you don't mind me asking the following

1.

Are Mr Chunmei Chi and Mr Feng Gao provide some sort of script, to help you up to speed? or do you have to write the script on your own?

2.

How are you going to connect this

to the expression shown in your question?

there's still a pole 1/(x-t) right on the edge of the integration interval.

3.

Precisely to develop the fractional derivatives, Mr Chi and Mr Gao assume f(x) to have the following shape

this particular constraint on f(x) allows the application of the Fourier transform to carry on.

Do you need further assistance for this question?

If not, would you consider telling David to copy past the link as answer, and then you would consider clicking on the Accept Answer for the supplied link containing the solution?

Answer 1

[Walter Roberson]

https://www.mathworks.com/matlabcentral/fileexchange/45982-fractional-derivative

https://www.mathworks.com/matlabcentral/fileexchange/52587-fractional-derivative-and-integral

https://www.mathworks.com/matlabcentral/fileexchange/45877-fractional-differentiation-and-integration