On analysing discrete sequential operators of fractional order and their monotonicity results

In this study, we consider the analysis of monotonicity for the Riemann-Liouville fractional differences of sequential type. The results are defined on the subsets of (0, 1)×(0, 1) with a certain restriction. By analysing the difference operator in the point-wise form into a delta form, we use the standard sequential formulas as stated in Theorems 2.1 and 2.2 to establish the positivity of the delta difference operator of the proposed the discrete sequential operators. Finally, some numerical experiments are conducted which confirm our theoretical monotonicity results.