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Variation of constant formulas for fractional difference equations

Anh P. T., Babiarz A., Czornik A., Niezabitowski M., Siegmund S.

Archives of Control Sciences

2018

Vol. 28, No. 4

617--633

In this paper, we establish variation of constant formulas for both Caputo and Riemann-Liouville fractional difference equations. The main technique is the Z-transform. As an application, we prove a lower bound on the separation between two different solutions of a class of nonlinear scalar fractional difference equations.

Cone solutions of multi-order fractional difference systems

Girejko E., Mozyrska D.

Control and Cybernetics

2013

Vol. 42, no. 2

419--429

The fractional difference system of equations with different fractional orders is considered. We obtain the existence and uniqueness results for the initial value problem. Cone solutions are presented. An example is given to illustrate the results.