On a system of ( p , q ) -analogues of the natural transform for solving ( p , q ) -differential equations

Abstract

In this work, we apply the concept of (p, q)-calculus or post quantum calculus to establish the definitions of (p, q)-analogues of the natural transform of the first and second kind, which is a symmetric relation between (p, q)-analogues of the natural, Laplace, and Sumudu transforms. Moreover, as a result of the convolution theorem, some properties and some functions present in the table of (p, q)-analogues of the natural transform are discussed. Also, we apply them to solve higher order (p, q)-IVP with constants and coefficients, and to show the performance and effectiveness of the proposed transform.