From ControlTheoryPro.com

This section discusses inline functions, anonymous functions, and function handles. Each of these is portable in that rather than having to write an equation multiple times in a program, you can just define it once and then call it whenever you want to use it. In addition, function handles in particular allow you to pass an equation to another function for direct evaluation as needed. Inline and anonymous functions are useful for commandline evaluation or for multiple evaluations in the same mfile.
1 Inline functions
An inline function is one way that a function can be created at the command or in a script:
>>f = inline('2*x^23*x+4','x'); >>f(3) ans = 13
To create a multivariable inline function, send more inputs to the 'inline' function:
>> f = inline('2*x*y', 'x', 'y'); >> f(2,2) ans = 8
You cannot make an array of inline functions, MATLAB will tell you that you have too many inputs or do something weird like that.
2 Anonymous functions
A function can also be created at the command or in a script:
>>f = @(x) 2*x^23*x+4; >>f(3) ans = 13
To make an anonymous function of multiple variables, use a commaseparated list to declare the variables:
>>f = @(x,y) 2*x*y; >>f(2,2) ans = 8
It is possible to make an array of anonymous functions in MATLAB 7.1 but this will become outdated soon so using this construct in a distributed program is not recommended.
To pass anonymous functions to other functions, just use the name of the anonymous function in your call:
>> f = @(t,x) x; >> ode45(f, [0:15],1)
3 Function Handles
A function handle passes an mfile function into another function. This of course lets you have more control over what's passed there, and makes your program more general as it lets you pass any mfile (as long as it meets other requirements like having the right number of input arguments and so on).
To pass an mfile to a function, you must first write the mfile, say something like this:
function xprime = f(t,x) xprime = x;
Save it as myfunc.m. To pass this to another function, say an ODE integrator, use the @ symbol as follows:
>> ode45(@myfunc, [0:15], 1)
One advantage of using function handles over anonymous functions is that you can evaluate more than one equation in the mfile, thus allowing you to do things like solve systems of ODEs rather than only one. Anonymous functions limit you to one equation.