In this paper, we establish a lower bound on the separation between two distinct solutions of a scalar Riemann-Liouville fractional differential equation. As a consequence, we show that the Lyapunov exponent of an arbitrary non-trivial solution of a bounded linear scalar Riemann-Liouville fractional differential equation is always non-negative.

1.
K.
Diethelm
, The Analysis of Fractional Differential Equations. An Application-Oriented Exposition Using Differential Operators of Caputo Type, 
Lecture Notes in Mathematics
,
2004
,
Springer-Verlag
,
Berlin
,
2010
.
2.
A.A.
Kilbas
,
H.M.
Srivastava
and
J.J.
Trujillo
, Theory and Applications of Fractional Differential Equations,
North-Holland Mathematics Studies
,
204
.
Elsevier Science B.V.
,
Amsterdam
,
2006
.
3.
I.
Podlubny
, Fractional Differential Equations. An Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of their Solution and some of their Applications.
Mathematics in Science and Engineering
,
198
,
Academic Press, Inc.
,
San Diego, CA
,
1999
.
4.
D.
Idczak
,
R. Kamocki
,
On the existence and uniqueness and formula for the solution of R–L fractional Cauchy problem in Rn, Fractional Calculus and Applied Analysis
,
14
(
2011
),
538
553
.
5.
T.
Trif
,
Existence of solutions to initial value problems for nonlinear fractional differential equations on the semi-axis
,
Fractional Calculus and Applied Analysis
,
16
(
2013
),
595
612
.
6.
N.D.
Cong
,
T.S.
Doan
and
H.T.
Tuan
,
On fractional Lyapunov exponent for solutions of linear fractional differential equations
,
Fractional Calculus and Applied Analysis
,
17
(
2014
),
285
306
.
7.
N.D.
Cong
and
H.T.
Tuan
,
Generation of nonlocal fractional dynamical systems by fractional differential equations
,
Journal of Integral Equations and Applications
,
29
(
2017
),
585
608
.
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