An existence and uniqueness of mild solutions of fractional evolution problems

In this present paper, we concern to investigate the existence and uniqueness of mild solutions for a new class of fractional evolution problems involving sectorial operators and nonlocal conditions by means of fixed point theory. Here we use Caputo fractional derivative of order \(\varvec{\alpha }\) $\mathit{\alpha }$ with \({\textbf {2}}< \varvec{\alpha } < {\textbf {3}}\) $\mathbf{2}<\mathit{\alpha }<\mathbf{3}$ . In this sense, in order to elucidate the results obtained, we end the article with examples.