Acar, Nihan; Atıcı, Ferhan M. Exponential functions of discrete fractional calculus. (English) Zbl 1299.39001 Appl. Anal. Discrete Math. 7, No. 2, 343-353 (2013). Summary: Exponential functions of discrete fractional calculus with the nabla operator are studied. We begin with proving some properties of exponential functions along with some relations to the discrete Mittag-Leffler functions. We then study sequential linear difference equations of fractional order with constant coefficients. A corresponding characteristic equation is defined and considered in two cases where the characteristic real roots are the same or distinct. We define a generalized Casoratian for a set of discrete functions. As a consequence, for the solutions of sequential linear difference equations, their nonzero Casoratian ensures their linear independence. Cited in 26 Documents MSC: 39A12 Discrete version of topics in analysis 26A33 Fractional derivatives and integrals 33E12 Mittag-Leffler functions and generalizations 33B10 Exponential and trigonometric functions 39A06 Linear difference equations Keywords:discrete Mittag-Leffler functions; sequential fractional difference equations; exponential functions; linear difference equations; generalized Casoratian; linear independence PDFBibTeX XMLCite \textit{N. Acar} and \textit{F. M. Atıcı}, Appl. Anal. Discrete Math. 7, No. 2, 343--353 (2013; Zbl 1299.39001) Full Text: DOI