I was toying with equations of the type f(x+α)=f′(x) where f is a real function....
I was toying with equations of the type where f is a real function. For example if then the solutions include the function . Are there more solutions?
On the other hand, if I want to solve the equation for any , I can assume a solution of the form , and find as a complex number that enables me to solve the equation...
I was wondering: is the set of the solutions of dimension 2 because the derivative operator creates one dimension and the operator adds another one? Is there some litterature about this kind of equations?