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Sequential Differences In Nabla Fractional Calculus, Ariel Setniker

Department of Mathematics: Dissertations, Theses, and Student Research

We study the composition of nabla fractional differences of unequal orders, known as "sequential" nabla fractional differences. The sequential differences we examine possess different bases — specifically, we establish the outer operator as having a base larger than the inner operator by at least an integer factor of 1. Further, we consider two cases of orders: first the case when the outer difference has a larger power, and second when the inner difference has a larger power.

We develop rules for sequential nabla fractional differences and present connections between the sign of a sequential difference of a function and the …