Mixed order monotonicity results for sequential fractional nabla differences

We investigate sequential nabla fractional differences of the form ∇a+1ν∇aμf(t) in the case where 0<μ<1, 1<ν<2, and 1<μ+ν<2, as well as differences of the form ∇a+2ν∇aμf(t) in the case where 1<μ<2, 0<ν<1, and 1<μ+ν<2. We demonstrate connections between the sign of these fractional sequential differences and the monotonicity of the function f.