Weighted pseudo almost automorphic mild solutions for two-term fractional order differential equations

Using the notion of Weyl fractional derivative, we study the existence and uniqueness of weighted pseudo almost automorphic mild solutions for a class of two-term fractional order abstract differential equation in the form Dtαu′(t)+μDtβu(t)=Au(t)+Dtαf(t,u(t)),t≥0,0<α≤β≤1,μ≥0where A is a closed linear operator defined in a Banach space X and the forcing term f is Sp-weighted pseudo almost automorphic.