In this paper, I define Fibonacci function (probably unknown) on Real number field, for all x∈R, F:R → R,э F (x+n) = ∫nF(x+1)+∫n-1F(x). Also, I defined the limit value of Fibonacci function, which is closed to 1.618… where x tends to infinity. Including, Fibonacci sum as well.
Bulletin of Mathematical Sciences and Applications (Volume 1)
K. R. R. Gandhi "Exploration of Fibonacci Function", Bulletin of Mathematical Sciences and Applications, Vol. 1, pp. 57-62, 2012