Date:

2025-04-30

Title of Paper:

Cauchy problems for fractional differential equations with Riemann–Liouville fractional derivatives

Journal:

Journal of Functional Analysis

Summary:

In this paper, we are concerned with Cauchy problems of fractional differential equations with Riemann–Liouville fractional derivatives in infinite-dimensional Banach spaces. We introduce the notion of fractional resolvent, obtain some its properties, and present a generation theorem for exponentially bounded fractional resolvents. Moreover, we prove that a homogeneous α-order Cauchy problem is well posed if and only if its coefficient operator is the generator of an α-order fractional resolvent, and we give sufficient conditions to guarantee the existence and uniqueness of weak solutions and strong solutions of an inhomogeneous α-order Cauchy problem.

Co-author:

Kexue Li, Jigen Peng, Junxiong Jia

Volume:

263

Page Number:

476–510

Translation or Not:

No

Date of Publication:

2012-07-15