Two dimensional second order Fibonacci summation formula with extorial functions

Abstract

Abstract This paper aims to obtain the extorial type solutions for Fibonacci difference equations on real valued function defined in two dimensional space having shift value ℓ. Using two dimensional second order Fibonacci nabla difference operator and its inverse, we derived Second order fibonacci summation formula of product of real valued polynomial. A function obtained by replacing polynomial into polynomial factorials in the expansion of exponential function is called extorial function. Using extorial functions defined in ℝ2, we obtain solution of certain type of two dimensional second order difference equations. Suitable examples and numerical verifications are given to validate the findings.