On Hilfer Generalized Proportional Nabla Fractional Difference Operators

Abstract

In this paper, the Hilfer type generalized proportional nabla fractional differences are defined. A few important properties in the left case are derived and the properties in the right case are proved by Q-operator. The discrete Laplace transform in the sense of the left Hilfer generalized proportional fractional difference is explored. Furthermore, An initial value problem with the new operator and its generalized solution are considered.