zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
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.

34A08Fractional differential equations
34D05Asymptotic stability of ODE
Full Text: DOI