## 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
$D^{\alpha+1} x(t) + a(t) x(t) = 0,\quad 0 < \alpha <1,$
and determine sufficient conditions on the coefficient function $$a$$ such that the differential equation has a solution whose Riemann-Liouville derivative of order $$\alpha$$ converges to a finite limit as $$t\to\infty$$, and has a solution with a prescribed asymptotic behaviour of the form
$x(t) = (X_0 + O(1)) t^{\alpha-1} + (X_1 + o(1)) t^\alpha\text{ as }t\to\infty,$
where $$X_0$$ and $$X_1$$ are arbitrarily prescribed real numbers.

### MSC:

 34A08 Fractional ordinary differential equations 34D05 Asymptotic properties of solutions to ordinary differential equations
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### References:

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