Eur. Phys. J. Special Topics 226, 3391–3409 (2017)
https://doi.org/10.1140/epjst/e2018-00015-y

Regular Article

Properties of solution sets for Sobolev type fractional differential inclusions via resolvent family of operators

¹ School of Mathematics and Statistics, Xidian University, Xi’an 710071, Shaanxi, P.R. China
² Universidad de Talca, Instituto de Matemática y Física, Casilla 747, Talca, Chile

^a e-mail: lzchangyk@163.com

Received: 11 May 2017
Received in final form: 10 August 2017
Published online: 25 July 2018

Abstract

In this manuscript, by properties on some corresponding resolvent operators and techniques in multivalued analysis, we establish some results for solution sets of Sobolev type fractional differential inclusions in the Caputo and Riemann-Liouville fractional derivatives with order 1 < α < 2, respectively. We show that the solution sets are nonempty, compact, contractible and thus arcwise connected under some suitable conditions. We remark that our results are directly established through resolvent operators instead of subordination formulas usually applied, and the existence and compactness of E⁻¹ is not necessarily needed. Some applications are also given in the final.