On a new class of Atangana-Baleanu fractional Volterra-Fredholm integro-differential inclusions with non-instantaneous impulses

Abstract

• The existence of piecewise-continuous mild solution of Atangana-Baleanu fractional Volterra-Fredholm integro-differential inclusions with non-instantaneous impulses in Banach space is analyzed. • The Martelli’s fixed point theorem and r-resolvent operators are used. • An example is given to support the theoretical results. • The topic allows the deep theoretical investigation AB-derivatives. This manuscripts main objective is to examine the existence of piecewise-continuous mild solution of Atangana-Baleanu fractional Volterra-Fredholm integro-differential inclusions (ABFVFIDI) with non-instantaneous impulses (NII) in Banach space. Based on Martelli’s fixed point theorem and ρ -resolvent operators, we develop the main results. An example is given to support the validation of the theoretical results achieved.