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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.

Local controllability of nonlinear discrete-time fractional order systems

Mozyrska D., Pawłuszewicz E.

Bulletin of the Polish Academy of Sciences. Technical Sciences

2013

Vol. 61, nr 1

251-256

The Riemann-Liouville, Caputo and Gr¨unwald-Letnikov fractional order difference operators are discussed and used to state and solve the controllability problem of a nonlinear fractional order discrete-time system. It is shown that independently of the type of fractional order difference, such a system is locally controllable in q steps if its linear approximation is globally controllable in q steps.