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.


39A06 Linear difference equations
39A12 Discrete version of topics in analysis
26A33 Fractional derivatives and integrals
34A08 Fractional ordinary differential equations
Full Text: DOI


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