We consider a Cauchy problem for a fractional semilinear differential inclusions involving Caputo’s fractional derivative in non separable Banach spaces under Filippov type assumptions and we prove the existence of solutions. MSC: 34A60, 26A33, 34B15 keywords: fractional derivative, fractional semilinear differential inclusion, Lusin measurable multifunctions.

and Applied Analysis 3 is called the Riemann-Liouville fractional integral of h of order α > 0 when the right side exists. Here Γ is the usual Gamma function

We study the numerical approximation of boundary optimal control problems governed by semilinear elliptic partial differential equations with pointwise constraints on the control. The control is the trace of the state on the boundary of the domain, which is assumed to be a convex, polygonal, open set in R. Piecewise linear finite elements are used to approximate the control as well as the state...

Let Ω ⊂ RN be the upper half strip with a hole. In this paper, we show there exists a positive higher energy solution of semilinear elliptic equations in Ω and describe the dynamic systems of solutions of equation (1) in various Ω. We also show there exist at least two positive solutions of perturbed semilinear elliptic equations in Ω.