Valentin Keyantuo, Carlos Lizama, Mahamadi Warma
Abstract:
We study the solvability of the fractional order inhomogeneous
Cauchy problem
where A is a closed linear operator in
some Banach space X and
a given function.
Operator families associated with this problem are defined and
their regularity properties are investigated. In the case where
A is a generator of a
-times
integrated cosine family
,
we derive explicit representations of mild and
classical solutions of the above problem in terms of the
integrated cosine family. We include applications to elliptic
operators with Dirichlet, Neumann or Robin type boundary
conditions on
-spaces
and on the space of continuous
functions.
Submitted October 26, 2016. Published September 18, 2017.
Math Subject Classifications: 47D06, 35K20, 35L20, 45N05.
Key Words: Fractional derivative; subordination principle; elliptic operator;
integrated cosine family; Dirichlet,
Neumann and Robin boundary conditions.
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Valentin Keyantuo University of Puerto Rico, Department of Mathematics Faculty of Natural Sciences Rio Piedras Campus, P.O. Box 70377 San Juan, PR 00936-8377, USA email: valentin.keyantuo1@upr.edu | |
Carlos Lizama Universidad de Santiago de Chile Departamento de Matemática Facultad de Ciencias Casilla 307-Correo 2, Santiago, Chile email: carlos.lizama@usach.cl | |
Mahamadi Warma University of Puerto Rico Department of Mathematics Faculty of Natural Sciences Rio Piedras Campus, P.O. Box 70377 San Juan, PR 00936-8377, USA email: mjwarma@gmail.com, mahamadi.warma1@upr.edu |
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