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

Abstract In this article, we show sufficient conditions ensuring the existence and uniqueness of pseudo almost automorphic solution using measure theory to the two-term fractional order differential equation in the form{equation*} Dₜαu'(t)+γ Dₜβu(t)= Au(t)+Dₜαf(t,u(t)), t,0<α β < 1,γ 0.{equation*}Where \(A\) is a sectorial operator of angle \(β π/2\) , the fractional derivative is understood in the Weyl sense and the forcing term \(f\) of the equation is \(μ\) -Stepanov-like pseudo almost automorphic function, μ is a positive measure on \(R\) . An example is given for illustration.