Exponential functions of discrete fractional calculus. (English) Zbl 1299.39001

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.


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
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