How to fit my data with an array instead of standard functions?

I have an x-data and y-data as an array. I want to fit it with another function made from another array instead of standard functions like 'poly2' etc. Here is a simplified example of the problem. In my work the fitting function may not be any standard function (i.e. which cannot be written analytically).

x=[0;1;2;3;4;5;6;7;8;9;10]; %x Data

y=[0;1;3;9;16;23;36;50;64;84;99]; %y Data


f=fit(x,y,'poly2') % standard way of fitting

plot(f,x,y) %plotting the fit

%% Instead of 'poly2' I want to use fit_funtion to fit my data which is made of an array of data points, z
% z=[0;1;4;9;16;25;36;49;64;81;100]
% fit_funtion= p1*z.^2+p2*z+p3 % p1, p2, p3 are the coefficients to fit

Instead of 'poly2' I want to use fit_funtion to fit my data which is made of an array of data points, z

z=[0;1;4;9;16;25;36;49;64;81;100]

and my fitting function is made of a combination of z as below

fit_funtion=

where p1, p2, p3 are the coefficients to fit.

Is there any technique availabe in MATLAB to do this kind of fitting?

[Torsten]

Look at the examples

Fit a Curve Defined by a File

or

Fit a Custom Model Using an Anonymous Function

under

https://de.mathworks.com/help/curvefit/fit.html