Non-autonomous fractional Cauchy problems with almost sectorial operators

In this paper, we study a class of non -autonomous fractional Cauchy problems with the almost sectorial operators. We consider the time fractional derivative in the sense of Caputo type. First, we construct two operator families by means of Mittag-Leffler functions, which will be useful to both determine the structure of solution operator families and prove existence results. Moreover, we establish the existence and uniqueness for classical solutions of linear problem, and the existence of mild solutions for nonlinear problem by proving the compactness of solution operator families. Finally, we provide several examples to illustrate the efficiency of our results. (c) 2024 Elsevier Masson SAS. All rights reserved.