ASYMPTOTIC BEHAVIOR OF NABLA HALF ORDER H-DIFFERENCE EQUATIONS

Baoguo Jia; Feifei Du; Lynn Erbe; Allan Peterson

doi:10.11948/2018.1707

2018 Volume 8 Issue 6

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Baoguo Jia, Feifei Du, Lynn Erbe, Allan Peterson. ASYMPTOTIC BEHAVIOR OF NABLA HALF ORDER H-DIFFERENCE EQUATIONS[J]. Journal of Applied Analysis & Computation, 2018, 8(6): 1707-1726. doi: 10.11948/2018.1707

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Baoguo Jia, Feifei Du, Lynn Erbe, Allan Peterson. ASYMPTOTIC BEHAVIOR OF NABLA HALF ORDER H-DIFFERENCE EQUATIONS[J]. Journal of Applied Analysis & Computation, 2018, 8(6): 1707-1726. doi: 10.11948/2018.1707

ASYMPTOTIC BEHAVIOR OF NABLA HALF ORDER H-DIFFERENCE EQUATIONS

1 School of Mathematics, Sun Yat-sen University, 510275 Guangzhou, China;
2 Department of Mathematics, University of Nebraska-Lincoln, 68588-0130 Lincoln, USA

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Abstract

Abstract

In this paper we study the half order nabla fractional difference equation _ρ(a)∇_h^0.5x(t)=cx(t),t ∈ (hN)_a+h,where _ρ(a)∇_h^0.5x(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.
- Laplace transform /
- Mittag-Leffler function /
- Riemann-Liouville fractional h-difference /
- oscillation
MSC: 39A12;39A70

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References

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