Analysing discrete fractional operators with exponential kernel for positivity in lower boundedness

Abstract

In this paper we study the positivity analysis problems for discrete fractional operators with exponential kernel, namely the discrete Caputo-Fabrizio operators. The results are applied to a discrete Caputo-Fabrizio-Caputo fractional operator of order ω of another discrete Caputo-Fabrizio-Riemann fractional operator of order β. Furthermore, the results are obtained for these operators with having the same orders. The conditions for the discrete fractional operators with respect to negative lower bound conditions are expressed in terms of a positive epsilon.