Recently, there has been significant development in the existence of mild solutions for fractional semilinear integro-differential equations but optimal control is not provided. The aim of this paper is studying optimal feedback control for fractional semilinear integro-differential equations in an arbitrary Banach space associated with operators ...

This paper is concerned with the study of weighted pseudo almost periodic mild solutions for semilinear boundary differential equations. Namely, some sufficient conditions for the existence and uniqueness of weighted pseudo almost periodic mild solutions of semilinear boundary differential equations are obtain.

We present a uniform L-stability estimate for mild solutions to the Fokker-Planck-Boltzmann equation. For stability estimate, we derive a Gronwall type estimate using dispersion estimates for mild solutions due to the hypoelliptic structure of the Vlasov-Fokker-Planck operator.

In this investigation, our aim is to develop the definition of mild solutions for impulsive fractional differential equations of order α ∈ (1,2) and obtain some sufficient conditions for existence of mild solutions using the analytic operator functions and fixed point theorems. We also verify the existence result with an example involving partial derivative.