223 research outputs found
A generalization of Hukuhara difference for interval and fuzzy arithmetic
We propose a generalization of the Hukuhara difference. First, the case of compact convex sets is examined; then, the results are applied to generalize the Hukuhara difference of fuzzy numbers, using their compact and convex level-cuts. Finally, a similar approach is seggested to attempt a generalization of division for real intervals and fuzzy numbers.Fuzzy Arithmetic, Interval Arithmetic, Hukuhara difference, Fuzzy Numbers.
A differential calculus for multifunctions
Mathematical analysis of multifunction
A density theorem for parameterized differential Galois theory
We study parameterized linear differential equations with coefficients
depending meromorphically upon the parameters. As a main result, analogously to
the unparameterized density theorem of Ramis, we show that the parameterized
monodromy, the parameterized exponential torus and the parameterized Stokes
operators are topological generators in Kolchin topology, for the parameterized
differential Galois group introduced by Cassidy and Singer. We prove an
analogous result for the global parameterized differential Galois group, which
generalizes a result by Mitschi and Singer. These authors give also a necessary
condition on a group for being a global parameterized differential Galois
group; as a corollary of the density theorem, we prove that their condition is
also sufficient. As an application, we give a characterization of completely
integrable equations, and we give a partial answer to a question of Sibuya
about the transcendence properties of a given Stokes matrix. Moreover, using a
parameterized Hukuhara-Turrittin theorem, we show that the Galois group
descends to a smaller field, whose field of constants is not differentially
closed.Comment: To appear in Pacific Journal of Mathematic
A survey on fuzzy fractional differential and optimal control nonlocal evolution equations
We survey some representative results on fuzzy fractional differential
equations, controllability, approximate controllability, optimal control, and
optimal feedback control for several different kinds of fractional evolution
equations. Optimality and relaxation of multiple control problems, described by
nonlinear fractional differential equations with nonlocal control conditions in
Banach spaces, are considered.Comment: This is a preprint of a paper whose final and definite form is with
'Journal of Computational and Applied Mathematics', ISSN: 0377-0427.
Submitted 17-July-2017; Revised 18-Sept-2017; Accepted for publication
20-Sept-2017. arXiv admin note: text overlap with arXiv:1504.0515
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