On a solution to fractional order integrodifferential equations with analytic semigroups

Existence of Fractional Impulsive Functional Integro-Differential Equations in Banach Spaces

“…Finally, we would like to mention the recently published paper written by Liu and Ahmed [34], where the formula of solutions for semi-linear impulsive fractional Cauchy problems (see (20) in Ref. [34]) coincided with ours (see Definition 5), if one imposes that the semi-linear term and the impulsive term have the same expression in the given interval.…”

“…In recent years, impulsive integro-differential equations have become an important object of investigation stimulated by their numerous applications to problems in mechanics, electrical engineering, medicine, biology, ecology and so forth [14][15][16][17][18][19]. Gürbüz studied the estimation and behavior of a class of fractional type rough higher order commutators, sublinear operators, and multi-sublinear operators on generalized weighted Morrey spaces [20][21][22][23][24][25].…”

Periodic solutions of neutral fractional differential equations

“…On the other hand, because several important physical phenomena are modeled by abstract fractional differential equations this type of equations have been studied extensively last time for many authors. We refer the reader to the works and the references listed therein for recent information on this subject. For some applications of fractional differential equations, see .…”

Existence Results for Fractional Integro-Differential Equations with Fractional Order Non-instantaneous Impulsive Conditions

“…On the other hand, we came to know from the semigroup theory that many authors used the concept of mild solutions inappropriately, see [5,15,23,25]. To make the concept of mild solutions more appropriate, E. Hernández et.…”