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arXiv · 1502.06014

Conformable Fractional Semigroups of Operators

Mohammed AL Horani·Roshdi Khalil·Thabet Abdeljawad
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Abstract

Let $X$ be a Banach space, and $T:[0,\infty)\rightarrow {\mathcal{L}}(X,X),$ the bounded linear operators on $X.$ A family $\{T(t)\}_{t\ge 0}\subseteq {% \mathcal{L}}(X,X)$ 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.

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Mohammed AL Horani, Roshdi Khalil, Thabet Abdeljawad. 2014-11-21. Conformable Fractional Semigroups of Operators. https://arxiv.org/abs/1502.06014

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