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Asymptotic behavior of nabla half order $h$-difference equations
Keywords:Laplace transform, Mittag-Leffler function, Riemann-Liouville fractional $h$-difference, oscillation.
Abstract:
      In this paper we study the half order nabla fractional difference equation $ _{\rho(a)}\nabla^{0.5}_{h}x(t)=cx(t), ~ t\in(h\N)_{a+h},$ where $_{\rho(a)}\nabla^{0.5}_hx(t)$ denotes the Riemann-Liouville nabla half order $h$-difference of $x(t)$. We will establish the asymptotic behavior of the solutions of this equation satisfying $x(a)=A>0$ for various values of the constant $c$.