A Note on Fractional Semigroup Theory and Fractional Evolution Equations
Ndubuisi, R. U *
Department of Mathematics, Federal University of Technology, Owerri, Nigeria.
Holget, Chidiebere. G
Department of Mathematics, Federal University of Technology, Owerri, Nigeria.
Nwajeri, U. K
Department of Mathematics, Federal University of Technology, Owerri, Nigeria.
Kailash, M. Patil
Department of Mathematics, Dharmsinh Desai University, Nadiad-387001, India.
Okechukwu U. Solomon
Department of Physical Science, Rhema University, Aba, Abia State, Nigeria.
Ashara, Precious C.
Department of Mathematics, Federal University of Technology, Owerri, Nigeria.
Osuji, W.I
Department of Mathematics, Federal University of Technology, Owerri, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
This paper considers fractional semigroup theory and fractional evolution equations. First and foremost, we present some fractional semigroups and prove the semigroup property associated with Riemann-Liouville fractional integral operator which is not necessarily true for the fractional differential operator. Consequently, we utilize the fractional \(\beta\)-semigroup of operators to solve the fractional abstract Cauchy problem.
Keywords: Fractional β-semigroup, fractional Cauchy problem, Riemann-liouville operator