In this paper, we prove the existence of decay integral solutions to a class of fractional differential inclusions with finite delays and estimate their decay rate. For these purposes, we have to construct a suitable regular measure of noncompactness on the space of solutions and then deploy the fixed point theory for condensing multivalued maps. An application to a class of fractional PDE with almost sectorial operator is also given.
"Decay Solutions and Decay Rate for a Class of Retarded Abtract Semilinear Fractional Evolution Inclusions." Taiwanese J. Math. 23 (3) 625 - 651, June, 2019. https://doi.org/10.11650/tjm/181101