Alpha-Delta Integration and Its Application in Discrete Kinetic Equation Using Mittag–Leffler Factorial Function

Abstract

The summation and exact form of the solutions related to the special type of difference equations are established in this paper by using the inverse of the delta and alpha-delta operators. As an application, the solutions of the population growth model, particularly, fractional order kinetic equation, are obtained by this method. Also, by using the summation form and Mittag–Leffler factorial functions, the alpha-delta integrations have been applied for solving the fractional order difference equations involving the factorial polynomials. Numerical examples are provided to validate the theoretical results.