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On the solution set for a class of sequential fractional differential equations. (English) Zbl 1216.34004

The authors consider the linear homogeneous Riemann-Liouville fractional differential equation with non-constant coefficients

D α+1 x(t)+a(t)x(t)=0,0<α<1,

and determine sufficient conditions on the coefficient function a such that the differential equation has a solution whose Riemann-Liouville derivative of order α converges to a finite limit as t, and has a solution with a prescribed asymptotic behaviour of the form

x(t)=(X 0 +O(1))t α-1 +(X 1 +o(1))t α ast,

where X 0 and X 1 are arbitrarily prescribed real numbers.

MSC:
34A08Fractional differential equations
34D05Asymptotic stability of ODE