2,951 research outputs found
Qualitative analysis of dynamic equations on time scales
In this article, we establish the Picard-Lindelof theorem and approximating
results for dynamic equations on time scale. We present a simple proof for the
existence and uniqueness of the solution. The proof is produced by using
convergence and Weierstrass M-test. Furthermore, we show that the Lispchitz
condition is not necessary for uniqueness. The existence of epsilon-approximate
solution is established under suitable assumptions. Moreover, we study the
approximate solution of the dynamic equation with delay by studying the
solution of the corresponding dynamic equation with piecewise constant
argument. We show that the exponential stability is preserved in such
approximations.Comment: 13 page
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
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
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