Bounded mild solutions to fractional integro-differential equations in Banach spaces

Weighted pseudo antiperiodic solutions for fractional integro-differential equations in Banach spaces

“…We recall the following definition [16] (see also [17] for a general treatment on resolvent families). …”

“…Usually, papers working on the subject consider only fractional derivatives in the sense of Riemann-Liouville and Caputo. However, it has been showed recently in the reference [16] that concerning bounded solutions of fractional evolution equations on the line, the right concept should be those of fractional derivative in the Weyl's sense. In such way mild solutions can be strong solutions (for sufficiently smooth forcing terms), which is not the case for equations with fractional derivatives posed in the sense of Riemann-Liouville or Caputo.…”

“…Eq. (1.1) with L defined by (1.2) has been studied in [16]. The study of existence of solutions to such class of fractional differential equations is an important topic due to its significance and applications in physics, probability, modeling, mechanics and other areas.…”

Existence Results for a Family of Equations of Fractional Resolvent

“…Numerous researchers established the existence and uniqueness of m-solution for different types of fractional differential equations and differential-integral equations (Agarwal et al 2012;Cuevas & Lizama 2008;Diagana 2009;Ponce 2013). Furthermore, Cuevas and Lizama (2008) elected almost mild solutions for:…”

“…Agarwal et al (2012) studied analytic resolvent operator and existence results for fractional integro-differential equations of the form: Ponce (2013) considered the presence and distinction of bounded solutions for the linear fractional differential equation:…”