Analytic Conformable Semigroups and Regularity of Solutions to Conformable Fractional Cauchy Problem

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Bambang Hendriya Guswanto, Sri Maryani, Najmah Istikaanah

Abstract

We introduce an analytic conformable semigroup which is a solution operator of an evolution equation involving conformable fractional derivative and a sectorial linear operator. The evolution equation is called a conformable fractional Cauchy problem. We here also derive the properties of the analytic conformable semigroup by employing the properties of the analytic semigroup. The analytic conformable semigroup is then used to study the regularity of solutions to the conformable fractional Cauchy problem under Hölder continuity as a regularity condition. An example is given to show the applicability of our regularity results.

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