Baleanu, DumitruMustafa, Octavian G.Agarwal, Ravi P.2020-05-162020-05-162011Bleanu, D.; Mustafa, O.G.; Agarwal, R.P.,"Asymptotic Integration of (1 + Α) -Order Fractional Differential Equations",Vol. 62, No. 3, pp. 1492-1500, (2011).8981221http://hdl.handle.net/20.500.12416/3873We establish the long-time asymptotic formula of solutions to the (1+α)-order fractional differential equation 0iOt1+αx+a(t)x=0, t>0, under some simple restrictions on the functional coefficient a(t), where 0iOt1+α is one of the fractional differential operators 0Dtα(x′), (0Dtαx)′= 0Dt1+αx and 0Dtα(tx′-x). Here, 0Dtα designates the Riemann-Liouville derivative of order α∈(0,1). The asymptotic formula reads as [b+O(1)] ·xsmall+c·xlarge as t→+∞ for given b, c∈R, where xsmall and xlarge represent the eventually small and eventually large solutions that generate the solution space of the fractional differential equation 0iOt1+αx=0, t>0eninfo:eu-repo/semantics/openAccessLinear Fractional Differential EquationAsymptotic IntegrationArticle6231492150010.1016/j.camwa.2011.03.021