11,514 research outputs found
Enlarged Controllability of Riemann-Liouville Fractional Differential Equations
We investigate exact enlarged controllability for time fractional diffusion
systems of Riemann-Liouville type. The Hilbert uniqueness method is used to
prove exact enlarged controllability for both cases of zone and pointwise
actuators. A penalization method is given and the minimum energy control is
characterized.Comment: This is a preprint of a paper whose final and definite form is with
'Journal of Computational and Nonlinear Dynamics', ISSN 1555-1415, eISSN
1555-1423, CODEN JCNDDM, available at
[http://computationalnonlinear.asmedigitalcollection.asme.org]. Submitted
10-Aug-2017; Revised 28-Sept-2017 and 24-Oct-2017; Accepted 05-Nov-201
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
Semi-Markov models and motion in heterogeneous media
In this paper we study continuous time random walks (CTRWs) such that the
holding time in each state has a distribution depending on the state itself.
For such processes, we provide integro-differential (backward and forward)
equations of Volterra type, exhibiting a position dependent convolution kernel.
Particular attention is devoted to the case where the holding times have a
power-law decaying density, whose exponent depends on the state itself, which
leads to variable order fractional equations. A suitable limit yields a
variable order fractional heat equation, which models anomalous diffusions in
heterogeneous media
On the analysis of mixed-index time fractional differential equation systems
In this paper we study the class of mixed-index time fractional differential
equations in which different components of the problem have different time
fractional derivatives on the left hand side. We prove a theorem on the
solution of the linear system of equations, which collapses to the well-known
Mittag-Leffler solution in the case the indices are the same, and also
generalises the solution of the so-called linear sequential class of time
fractional problems. We also investigate the asymptotic stability properties of
this class of problems using Laplace transforms and show how Laplace transforms
can be used to write solutions as linear combinations of generalised
Mittag-Leffler functions in some cases. Finally we illustrate our results with
some numerical simulations.Comment: 21 pages, 6 figures (some are made up of sub-figures - there are 15
figures or sub-figures
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