62 research outputs found
Monotone iterative procedure and systems of a finite number of nonlinear fractional differential equations
The aim of the paper is to present a nontrivial and natural extension of the
comparison result and the monotone iterative procedure based on upper and lower
solutions, which were recently established in (Wang et al. in Appl. Math. Lett.
25:1019-1024, 2012), to the case of any finite number of nonlinear fractional
differential equations.The author is very grateful to the reviewers for the remarks, which improved the final version of the manuscript. This
article was financially supported by University of Łódź as a part of donation for the research activities aimed at the
development of young scientists, grant no. 545/1117
Killing Tensors and Conformal Killing Tensors from Conformal Killing Vectors
Koutras has proposed some methods to construct reducible proper conformal
Killing tensors and Killing tensors (which are, in general, irreducible) when a
pair of orthogonal conformal Killing vectors exist in a given space. We give
the completely general result demonstrating that this severe restriction of
orthogonality is unnecessary. In addition we correct and extend some results
concerning Killing tensors constructed from a single conformal Killing vector.
A number of examples demonstrate how it is possible to construct a much larger
class of reducible proper conformal Killing tensors and Killing tensors than
permitted by the Koutras algorithms. In particular, by showing that all
conformal Killing tensors are reducible in conformally flat spaces, we have a
method of constructing all conformal Killing tensors (including all the Killing
tensors which will in general be irreducible) of conformally flat spaces using
their conformal Killing vectors.Comment: 18 pages References added. Comments and reference to 2-dim case.
Typos correcte
Nonlinear fractional differential equations in nonreflexive Banach spaces and fractional calculus
The aim of this paper is to correct some ambiguities and inaccuracies in Agarwal et al. (Commun. Nonlinear Sci. Numer. Simul. 20(1): 59-73, 2015; Adv. Differ. Equ. 2013: 302, 2013, doi:10.1186/1687-1847-2013-302) and to present new ideas and approaches for fractional calculus and fractional differential equations in nonreflexive Banach spaces
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