On Hilfer Generalized Proportional Nabla Fractional Difference Operators

Qiushuang Wang and Run Xu
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Qiushuang Wang: School of Mathematical Sciences, Qufu Normal University, Qufu 273165, China
Run Xu: School of Mathematical Sciences, Qufu Normal University, Qufu 273165, China

Mathematics, 2022, vol. 10, issue 15, 1-16

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.

Keywords: hilfer operator; generalized proportional fractional difference; Q -operator; discrete laplace transform; the initial value problem (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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