Fractional Supershifts and their associated Cauchy Evolution problems

TL;DR

This paper extends supershifts and superoscillation sequences to fractional Fock spaces using Gelfond-Leontiev derivatives, and explores the associated fractional evolution Cauchy problems with these supershifts as initial conditions.

Contribution

It introduces fractional supershifts in Fock spaces and analyzes their role in fractional evolution Cauchy problems, a novel extension of existing concepts.

Findings

Defined fractional supershifts in Gelfond-Leontiev fractional Fock spaces

Formulated the associated fractional evolution Cauchy problem

Provided initial conditions based on fractional supershifts

Abstract

In this work, we extend the notion of supershifts and superoscillation sequence to fractional Fock spaces based on Gelfond-Leontiev fractional derivatives. We first introduce the fractional supershifts sequence, and then discuss the associated evolution Cauchy problem with the fractional supershifts as initial condition.