Memory is the key to our life. Already in 1870, the famous physiologist Hering (1) stated in a booklet that memory “connects innumerable single phenomena into a whole, and just as the body would be scattered like dust in countless atoms if the attraction of matter did not hold it together so consciousness – without the connecting power of memory – would fall apart in as many fragments as it con...

The existence of mild solutions for Hilfer fractional evolution equations with nonlocal conditions in a Banach space is investigated this manuscript. No assumptions about the compactness function or Lipschitz continuity nonlinear are imposed on item and function, respectively. However, we assumed that continuous, term continuous satisfies some specified assumptions, associated semigroup compact...

In this paper, we present a new type of Gronwall inequality and discuss some particular cases. We apply these results to investigate the uniqueness δ-Ulam–Hyers–Rassias stability mild solutions fractional differential equation with non-instantaneous impulses in Pδ-normed Banach space. sense, an example, order elucidate one discussed.