Analytic General Conformable Semigroup

Conformable fractional derivative is introduced by [1] to simplify the definition of fractional derivatives since most of them used an integral form which is difficult to solve real problem. However, [1] defined the conformable fractional derivative by considering a particular conformable fractional function t1−α. In this study, general conformable fractional Cauchy problem is considered and solved by using general conformable Laplace transform to obtain the solution operator of general conformable fractional Cauchy problem. Properties of classical semigroup are employed to retrieve the properties of general conformable semigroup from the solution operator of general conformable fractional Cauchy problem. Consequently, general conformable semigroup properties can be used to detemine the regularity of general conformable fractional Cauchy problem including its existence and uniqueness of the solution.