Baleanu, DumitruMustafa, Octavian G.Agarwal, Ravi P.2020-04-152020-04-152011Baleanu, Dumitru; Mustafa, Octavian G.; Agarwal, Ravi P. " Asymptotic integration of (1+alpha)-order fractional differential equations", Computers & Mathematics With Applications, Vol. 62, No. 3, pp. 1492-1500, (2011)0898-1221https://hdl.handle.net/20.500.12416/3142We 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. (C) 2011 Elsevier Ltd. All rights reserved.eninfo:eu-repo/semantics/openAccessLinear fractional differential equationAsymptotic integrationArticle10.1016/j.camwa.2011.03.021