The purpose of this paper is to establish the well-posedness and the regularity of solutions of the initialboundary value problems for general higher order parabolic equations in infinite cylinders with the bases containing conical points.

Communicated by M. KiraneOur aim in this work is to find decay integral solutions for a class of neutral fractional differential equations in Banach spaces involving unbounded delays. By constructing a suitable measure of noncompactness on the space of solutions and establishing new estimates for fractional resolvent operators, we prove the existence of a compact set of decay integral solutions to the mentioned problem.deriving new estimates for fractional resolvent operators, constructing a satisfactory space of solutions and find on this space a regular measure of noncompactness (MNC).These features enable us to utilize the fixed point theory for condensing maps. Consequently, we obtain the existence of decay integral solutions x with kx.t/k D O .t ˛/ as t ! 1. Because the case˛2 .0, 1/ is more involved than the case˛D 1, we focus on the former one and make a note that our technique can be applied to the latter case with the same manner. (B*) The phase space B satisfies (B) with K 2 BC R C ; R C and M being such that t M.t/ D O.1/ as t ! 1. (H*) The function h verifies (H) for all T > 0 and for Á 2 BC R C , R C . In addition, h.t, 0/ D 0 for all t 2 R C . (F*) f satisfies (F) for all T > 0. Put Á 1 D sup t 0 Á.t/, K 1 D sup t 0 K.t/, and M 1 D sup t 0 M.t/.

In this paper, we deal with the second initial boundary value problem for higher order hyperbolic systems in domains with conical points. We establish several results on the well-posedness and the regularity of solutions.

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