Conformable Fractional Semigroups of Operators

By M. Horani, Roshdi Khalil, Thabet Abdeljawad. 2014

97 citations recorded by the source corpus.

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.

Subfields: Applied Mathematics

View Paper: https://www.semanticscholar.org/paper/2c27bd4453f0153285b0107b74cc58b9f2e0906c

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In Applied Mathematics

Citations in the corpus

Newly Defined Conformable Derivatives (2015, background): “Several follow-up papers using at least one of the above conformable definitions include [2–8, 10–13, 19].”