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When do fractional differential equations have solutions bounded by the Mittag-Leffler function?
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When do fractional differential equations have solutions on the half line
that are bounded by the Mittag–Leffler function?
This work answers the above question through fixed–point methods,
providing a deeper understanding of the long term growth behaviour of
solutions, in addition to advancing our knowledge on the existence and
uniqueness of solutions.
Motivated by the above, this work answers the question posed at the
start of this section through a strategic analysis and application of complete
metric spaces and fixed–point theory. In particular, a novel metric is introduced
that involves the Mittag–Leffler function. When coupled with the
“Mittag–Leffler bounded” space of continuous functions on the half–line,
we show that the pair forms a complete metric space.
We then formulate sufficient conditions under which an integral problem
that is equivalent to our problem will admit a unique solution. This is
achieved via an application of the contraction mapping theorem of Stefan
Banach.
that are bounded by the Mittag–Leffler function?
This work answers the above question through fixed–point methods,
providing a deeper understanding of the long term growth behaviour of
solutions, in addition to advancing our knowledge on the existence and
uniqueness of solutions.
Motivated by the above, this work answers the question posed at the
start of this section through a strategic analysis and application of complete
metric spaces and fixed–point theory. In particular, a novel metric is introduced
that involves the Mittag–Leffler function. When coupled with the
“Mittag–Leffler bounded” space of continuous functions on the half–line,
we show that the pair forms a complete metric space.
We then formulate sufficient conditions under which an integral problem
that is equivalent to our problem will admit a unique solution. This is
achieved via an application of the contraction mapping theorem of Stefan
Banach.
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