Impulsive problems for semilinear differential equations with nonlocal conditions

On the new concept of solutions and existence results for impulsive fractional evolution equations

“…As we all known, the nonlocal conditions has a better effect on the solution and is more precise for physical measurements than the classical initial condition alone. For the nonlocal impulsive Cauchy problems, we refer the readers to [9,10,11,17] and the references therein.…”

“…For a wide bibliography and exposition on this object see for instance the monographs of [1,2,3,4] and the papers [5,6,7,8,9,10,11,12,13,14,15,16,17,18,19].…”

Existence and controllability of fractional evolution equation with sectorial operator and impulse

“…For the fractional differential equations with nonlocal conditions, we refer to [18,23,42]. For the fractional differential equations with nonlocal conditions and impulsive effects, we refer to [13,14,21,37].…”

Existence results for impulsive differential equations with nonlocal conditions via measures of noncompactness

“…[6,7,8,13,17,18,19,23,28]. It is more precise for describing nature phenomena than the classical condition since more information is taken into account, thereby decreasing the negative effects incurred by a possibly erroneous single measurement taken at the initial time.…”

“…Very recently, Z. Fan [19] obtained the existence of mild solutions for the following impulsive semilinear differential equation…”