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Zbl 1216.34004
Băleanu, Dumitru; Mustafa, Octavian G.; Agarwal, Ravi P.
On the solution set for a class of sequential fractional differential equations. (English)
[J] J. Phys. A, Math. Theor. 43, No. 38, Article ID 385209, 7 p. (2010). ISSN 1751-8113; ISSN 1751-8121/e

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.
[Kai Diethelm (Braunschweig)]

MSC 2000:: *34A08
34D05 Asymptotic stability of ODE

Keywords: fractional differential equation; Riemann-Liouville derivative; asymptotic behaviour

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