Conformable fractional semigroups of operators

Thabet Abdeljawad, Mohammed AL Horani, Roshdi Khalil

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.

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Published: 2015-09-28

How to Cite this Article:

Thabet Abdeljawad, Mohammed AL Horani, Roshdi Khalil, Conformable fractional semigroups of operators, Journal of Semigroup Theory and Applications, Vol 2015 (2015), Article ID 7

Copyright © 2015 Thabet Abdeljawad, Mohammed AL Horani, Roshdi Khalil. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Journal of Semigroup Theory and Applications

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