Existence and controllability for nonlinear fractional differential inclusions with nonlocal boundary conditions and time-varying delay

Abstract This paper discusses the existence and controllability of a class of fractional order evolution inclusions with time-varying delay. In the weak topology setting we establish the existence of solutions. Then the controllability of this system with a nonlocal condition is established by applying the Glicksberg-Ky Fan fixed point theorem. As an application, nonlocal problems of a fractional reaction-diffusion equation with a discontinuous nonlinear term is examined.

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