Erratum to: Local stable manifold theorem for fractional systems
Erratum to: Nonlinear Dyn
Erratum to: Local stable manifold theorem for fractional systems
Amey Deshpande 0
Varsha DaftardarGejji 0
E p 0
(t p J j ) = t 0
B j 0
C j 0
hence 0
0 A. Deshpande Department of Mathematics, College of Engineering Pune , Pune 411005 , India
where B j (t ) and C j (t ) are n j × n j matrices defined as

E p,β (t p A)n×n = t 1−β B(t ) + C (t ), ”
is incorrect. The corrected version of the above
expression is presented below. Note that Lemma 4 part 1
remains as it is.
For the corrected expression, we introduce the
following notations. Notation: Let Iγ denote n j × n j
matrix with entries [Iγ ]i,k = δi+γ,k , (γ = 0, . . . , n j −
1, 1 ≤ i, k ≤ n j ).
Lemma 4 (Part 2 (Corrected)) For 0 < p < 1, j =
1, 2 . . . , l and q ∈ N\{1},
E p, p(t p J j ) = t − p B j (t ) + C j (t ),
B j (t ) := 0 j = 1, 2, . . . , s,
B j (t ) :=
C j (t ) :=
(t, λ j )In j −1 j = 1, 2, . . . , l,
1 ∂m+1 1
ψm (t, λ j ) = m! ∂λm+1 exp t λ jp
k=2
q (−1)m+2(k + m)! λ −jk−m−1t − pk
(k − 1)!
(1 − pk)
+ O(λ j −q−m t − p− pq ) .
Let B(t ) and C (t ) denote the block diagonal matrices
consisting of B j (t ) and C j (t ) on the diagonal,
respectively. Hence E p, p(t p A) = t − p B(t ) + C (t ).
As a consequence of the above correction,
appropriate changes should be made in expressions of Lemma
5, 6, 8 and the step II of the proof of the theorem. Thus
in view of these corrections the proof of the local
stable manifold theorem given by us in the original article
continues to hold true. For details we refer the readers
to our article [1].
1. Deshpande , A. , DaftardarGejji , V. : Local Stable Manifold theorem for fractional systems revisited . ArXiv eprints ( 2017 ). http://adsabs.harvard.edu/abs/ 2017arXiv170100076D