Fractional relaxation equations on Banach spaces

Abstract. We study existence and qualitative properties of solutions for the abstract fractional relaxation equation (0.1) u (t) - AD t u(t) + u(t) = f(t), 0 < < 1, t 0, u(0) = 0, on a complex Banach space X, where A is a closed linear operator, D t is the Caputo derivative of fractional order (0, 1), and f is an X-valued function. We also study conditions under which the solution operator has the properties of maximal regularity and Lp integrability. We characterize these properties in the Hilbert space case.

• Type: Journal
• Year: 2010
• Where: APPML
• Authors: Carlos Lizama, Humberto Prado
• Keywords: Abstract Fractional Relaxation, APPML 2010, Closed Linear Operator, Complex Banach Space