Abstract
In this paper, we introduce a fuzzy fractional semigroup of operators whose generator will be the fuzzy fractional derivative of the fuzzy semigroup at t = 0 . We establish some of their proprieties and some results about the solution of fuzzy fractional Cauchy problem.
Highlights
Fractional semigroups are related to the problem of fractional powers of operators initiated first by Bochner [1]
Balakrishnan [2] studied the problem of fractional powers of closed operators and the semigroups generated by them. e fractional Cauchy problem associated with a Feller semigroup was studied by Popescu [3]
Abdeljawad et al [4] studied the fractional semigroup of operators. e semigroup generated by linear operators of a fuzzy-valued function was introduced by Gal and Gal [5]
Summary
Fractional semigroups are related to the problem of fractional powers of operators initiated first by Bochner [1]. E semigroup generated by linear operators of a fuzzy-valued function was introduced by Gal and Gal [5]. All definitions mentioned above satisfy the property that the fuzzy fractional derivative is linear. Harir et al [20] defined a new well-behaved simple fractional derivative called “the fuzzy conformable fractional derivative” depending just on the basic limit definition of the derivative. We introduce the fuzzy fractional semigroups of operators associated with the fuzzy conformable fractional derivative, for proving to be a very fruitful tool to solve. En, we show that this semigroup is a solution to the fuzzy fractional Cauchy problem x(q)(t) f(x(t)), x(0) x0, and q ∈ International Journal of Differential Equations differential equations. en, we show that this semigroup is a solution to the fuzzy fractional Cauchy problem x(q)(t) f(x(t)), x(0) x0, and q ∈
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