Analytical and approximate monotone solutions of the mixed order fractional nabla operators subject to bounded conditions

Abstract

In this study, the sequential operator of mixed order is analysed on the domain [Formula: see text] with [Formula: see text]. Then, the positivity of the nabla operator is obtained analytically on a finite time scale under some conditions. As a consequence, our analytical results are introduced on a set, named [Formula: see text], on which the monotonicity analysis is obtained. Due to the complicatedness of the set [Formula: see text] several numerical simulations so are applied to estimate the structure of this set and they are provided by means of heat maps.

Keywords

• Nabla Riemann-Liouville fractional difference
• negative boundedness
• monotonicity analysis