A note on constructing sine and cosine functions in discrete fractional calculus

Asa Ashley; Ferhan M. Atıcı; Samuel Chang

doi:10.56754/0719-0646.2703.581

Authors

Asa Ashley Gatton Academy of Mathematics and Science, Bowling Green, Kentucky 42101 USA.
Ferhan M. Atıcı Department of Mathematics, Western Kentucky University, Bowling Green, Kentucky 42101-3576, USA. https://orcid.org/0000-0002-9862-9901
Samuel Chang Booth School of Business, University of Chicago, Chicago, Illinois 60637, USA. https://orcid.org/0000-0003-3730-2101

DOI:

https://doi.org/10.56754/0719-0646.2703.581

Keywords:

Discrete trigonometric functions, nabla operator, fractional h-discrete calculus, fractional difference equations, Picard's iteration

Abstract

In this paper, we introduce two sets of linear fractional order \(h\)-difference equations and derive their solutions. These solutions, referred to as trigonometric functions of fractional \(h\)-discrete calculus, are proven to have properties similar to sine and cosine functions on \(\mathbb{R}\). The illustrated graphs confirm these similarities.

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