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A fractional Laplace equation: Regularity of solutions and finite element approximations
(Society for Industrial and Applied Mathematics, 2017-01)
This paper deals with the integral version of the Dirichlet homogeneous fractional Laplace equation. For this problem weighted and fractional Sobolev a priori estimates are provided in terms of the Holder regularity of the ...
Smooth solutions to mixed-order fractional differential systems with applications to stability analysis
(Rocky Mountain Mathematics Consortium, 2019)
Conditions for existence, uniqueness and smoothness of solutions for systems of fractional differential equations of Caputo and/or Riemann-Liouville type having all of them in general and not of the same derivation order ...
Weighted inequalities and pointwise estimates for the multilinear fractional integral and maximal operators
(Academic Press Inc Elsevier Science, 2010-07)
In this article we prove weighted norm inequalities and pointwise estimates between the multilinear fractional integral operator and the multilinear fractional maximal. As a consequence of these estimations we obtain ...
Sharp Two weight inequalities for commutators of Riemann-Liouville and Weyl fractional integral operators
(Birkhauser Verlag Ag, 2008-08)
Let b be a BMO function, 0 < α < 1 and I+,k α,b the commutator of order k for the Weyl fractional integral. In this paper we prove weighted strong type (p, p) inequalities (p > 1) and weighted endpoint estimates (p = 1) ...