Conformable Fractional Semigroups of Operators
Abstract
Let
X
be a Banach space, and
T:[0,∞)→L(X,X),
the bounded linear operators on
X.
A family
{T(t)
}
t≥0
⊆L(X,X)
is called a one-parameter semigroup if
T(s+t)=T(s)T(t),
and
T(0)=I,
the identity operator on
X.
The infinitesimal generator of the semigroup is the derivative of the semigroup at
t=0.
The object of this paper is to introduce a (conformable) fractional semigroup of operators whose generator will be the fractional derivative of the semigroup at
t=0.
The basic properties of such semigroups will be studied.