Electron. J. Diff. Equ.,
Vol. 2016 (2016), No. 01, pp. 115.
Singular regularization of operator equations in L1 spaces via
fractional differential equations
George L. Karakostas, Ioannis K. Purnaras
Abstract:
An abstract causal operator equation y=Ay defined on a space of the
form
, with X a Banach space, is regularized
by the fractional differential equation
where
denotes the (left) RiemannLiouville derivative
of order
. The main procedure lies on properties of
the MittagLeffler function combined with some facts from convolution theory.
Our results complete relative ones that have appeared in the literature;
see, e.g. [5] in which regularization via ordinary differential
equations is used.
Submitted June 8, 2015. Published January 4, 2016.
Math Subject Classifications: 34K35, 34A08, 47045, 65J20.
Key Words: Causal operator equations; fractional differential equations;
regularization; Banach space.
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George L. Karakostas
Department of Mathematics
University of Ioannina
451 10 Ioannina, Greece
email: gkarako@uoi.gr


Ioannis K. Purnaras
Department of Mathematics
University of Ioannina
451 10 Ioannina, Greece
email: ipurnara@uoi.gr

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