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Linear systems of fractional nabla difference equations. (English) Zbl 1218.39003
The authors consider a system of linear fractional nabla difference equations with constant coefficients of the form $$\nabla_0^\nu y(t)=Ay(t)+f(t),\quad t=1,2,\dots,$$ where $A$ denotes an $n\times n$ matrix with constant entries, $0<\nu<1$ and $\nabla_0^\nu$ is the Riemann-Liouville fractional difference operator. They construct the fundamental matrix for the homogeneous system and the causal Green’s function for the nonhomogeneous system. Applications to asymptotic behavior are given.

MSC:
39A06Linear equations (difference equations)
39A12Discrete version of topics in analysis
26A33Fractional derivatives and integrals (real functions)
34A08Fractional differential equations
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References:
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