A class of the boundary value problem is investigated in this research work to prove the existence of solutions for the neutral fractional differential inclusions of Katugampola fractional derivative which involves retarded and advanced arguments. New results are obtained in this paper based on the Kuratowski measure of noncompactness for the suggested inclusion neutral system for the first time. On the one hand, this research concerns the set-valued analogue of Mönch fixed point theorem combined with the measure of noncompactness technique in which the right-hand side is convex valued. On the other hand, the nonconvex case is discussed via Covitz and Nadler fixed point theorem. An illustrative example is provided to apply and validate our obtained results.

在这项研究工作中，对一类边值问题进行了研究，以证明存在滞后论证和高级论证的Katugampola分数导数的中性分数微分包含解的存在。本文首次基于建议的包含中性系统的非紧致性的Kuratowski测度获得了新的结​​果。一方面，这项研究涉及Mönch不动点定理的集值模拟与非紧缩技术的度量相结合，其中右侧为凸值。另一方面，通过Covitz和Nadler不动点定理讨论了非凸情况。提供了一个说明性示例，以应用和验证我们获得的结果。