Asymptotic behavior of solutions of fractional nabla q-difference equations

作者：Jia, Baoguo; Erbe, Lynn; Peterson, Allan^*

来源：Georgian Mathematical Journal, 2019, 26(1): 21-28.

DOI：10.1515/gmj-2017-0030

• Nabla fractional q-difference
• generalized Gamma function
• fractional derivative

We are concerned with the v-th order nabla fractional q-difference equation (quantum equation) del(nu)(q,rho(1))x(t) = c(t)x(t), t is an element of q(N1), where q > 1, N-1 = (1, 2, ... }, rho(1) = q(-1). We prove that for 0 < nu < 1 and c(t) <= 0, t is an element of N-1, any solution of the q-difference equation with x(1) > 0 satisfies lim(t ->infinity) x(t) = 0. This asymptotic result shows that the solutions of the nabla fractional q-difference equation del(nu)(q,rho(1))x(t) = cx(t), 0 < nu < 1, c < 0, have asymptotic behavior similar to that of the solutions of the first order nabla q-difference equation del(q)x(t) = cx(t), c < 0, t is an element of q(N1).

• 出版日期2019-3
• 单位中山大学