This book is uniquely devoted to the theory of differential equations with non-instantaneous impulses. The authors investigate a wide class of differential equations with non-instantaneous impulses, including: - Ordinary differential equations with non-instantaneous impulses (scalar and n-dimensional case) - Fractional differential equations with non-instantenous impulses (with Caputo fractional derivatives of order q (0, 1)) - Ordinary differential equations with non-instantaneous impulses occurring at random moments (with exponential, Erlang, or Gamma distribution). An excellent examination of recent research on impulses in differential equations, this book presents three thorough chapters of theory, proofs, and examples that would interest graduate students and researchers in differential equations.