The Generalized Discrete Proportional Derivative and Its Applications

Abstract

The aim of this paper is to define the generalized discrete proportional derivative (GDPD) and illustrate the application of the Leibniz theorem, the binomial expansion, and Montmort’s formulas in the context of the generalized discrete proportional case. Furthermore, we introduce the generalized discrete proportional Laplace transform and determine the GDPLT of various functions using the inverse operator. The results obtained are showcased through relevant examples and validated using MATLAB.

Keywords

• fractional difference operator
• exact solution
• generalized polynomial factorial
• generalized discrete proportional Laplace transform
• numerical solution