Baleanu, DumitruMustafa, Octavian G.Agarwal, Ravi P.2017-02-172017-02-172011Baleanu, D...et al. (2011). Asymptotic integration of (1+alpha)-order fractional differential equations. Computers&Mathematics With Applications, 62(3), 1492-1500. http://dx.doi.org/10.1016/j.camwa.2011.03.0210898-1221http://hdl.handle.net/20.500.12416/1266We establish the long-time asymptotic formula of solutions to the (1 + alpha)-order fractional differential equation (i)(0)O(t)(1+alpha)x + a (t)x = 0, t > 0, under some simple restrictions on the functional coefficient a(t), where (i)(0)O(t)(1+alpha)x is one of the fractional differential operators D-0(t)alpha(x'), ((0)D(t)(alpha)x)' = D-0(t)1+alpha x and D-0(t)alpha(tx' - x). Here, D-0(t)alpha designates the Riemann-Liouville derivative of order a E (0, 1). The asymptotic formula reads as [b + O(1)] . x(small) + c . x(large) as t -> +infinity for given b, c E is an element of R, where x(small) and x(large) represent the eventually small and eventually large solutions that generate the solution space of the fractional differential equation (i)(0)O(t)(1+alpha)x = 0, t > 0.eninfo:eu-repo/semantics/closedAccessLinear Fractional Differential EquationAsymptotic IntegrationArticle6231492150010.1016/j.camwa.2011.03.021