An operational calculus model for the central difference and exponential-trigonometric and hyperbolic fibonacci sequences

In the paper, there has been constructed such a non-classical Bittner operational calculus model, in which the derivative is understood as a central difference D_n{x(k)}:= {x(k+n)–x(k-n)}. The discussed model has been generalized by considering the operation D_n,b{x(k)}:= {x(k+n)–bx(k-n)}, where b∈𝕔\{0}. In the D₁-difference model exponential-trigonometric and hyperbolic Fibonacci sequences have been introduced.