Bambang Hendriya Guswanto, Takashi Suzuki
Abstract:
In this article, we study the existence and uniqueness of a local mild solution
for a class of semilinear differential equations involving the Caputo
fractional time derivative of order
and, in the
linear part, a sectorial linear operator A. We put some conditions on a
nonlinear term f and an initial data
in terms of the fractional
power of A. By applying Banach's Fixed Point Theorem, we obtain a unique
local mild solution with smoothing effects, estimates, and a behavior at t
close to 0. An example as an application of our results is also given.
Submitted April 2, 2015. Published June 18, 2015.
Math Subject Classifications: 34A08, 34A12.
Key Words: Fractional semilinear differential equation; sectorial operator;
Caputo fractional derivative; fractional power; mild solution.
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Bambang Hendriya Guswanto Department of Mathematics Faculty of Mathematics and Natural Sciences Jenderal Soedirman University (UNSOED) Purwokerto, Indonesia email: bambanghg_unsoed@yahoo.com; bambang.guswanto@unsoed.ac.id | |
Takashi Suzuki Division of Mathematical Science Department of Systems Innovation Graduate School of Engineering Science Osaka University, Osaka, Japan email: suzuki@sigmath.es.osaka-u.ac.jp |
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