No abstract

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 . The discussed model has been generalized by considering the operation , where . In the -difference model exponential-trigonometric and hyperbolic Fibonacci sequences have been introduced.

In this paper, there has been constructed such a model of a non-classical Bittner operational calculus, in which the derivative is understood as a forward difference Δn{x(k)}:={x(k + n) – x(k)}. Next, considering the operation Δn,b{x(k)}:={x(k + n) – b x(k)}, the presented model has been generalized.

In the paper, there has been determined an exponential element in the discrete model of the non-classical Bittner operational calculus for the nth-order forward difference.

In this paper a form of the Taylor’s formula for the forward difference has been derived using the properties of the non-classical Bittner operational calculus.