发表机构
Punjab Engineering college (Deemed to be University)（旁遮邦工程学院（视为大学））
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文建立了统一两类经典分数积分的集值Katugampola分数积分理论，证明其保留集值映射的多种分析特性，且正则选择存在性可传递，拓展了分数积分在集值映射领域的应用。
AI 中文摘要
本文针对Katugampola分数积分，建立了集值映射的广义分数积分理论，该理论统一了经典的Riemann-Liouville和Hadamard分数积分。通过可积选择研究集值映射的Katugampola分数积分，探讨其关于R的非空紧子集空间上Hausdorff度量的性质，Katugampola分数积分保留了凸性、有界性和连续性等若干基本分析特性。此外，证明集值映射的有界变差和Lipschitz正则性在其Katugampola分数积分下均得以保留，研究了与Katugampola分数积分相关的正则选择的存在性，表明当原集值映射具有指定正则性的选择时，对应的Katugampola分数积分也具有该正则性。
英文摘要
In this paper, we develop a theory of generalized fractional integration for set-valued mappings for the Katugampola fractional integral, which unifies the classical Riemann-Liouville and Hadamard fractional integrals. The Katugampola fractional integral of a set valued mapping is studied using integrable selections. We study its properties with respect to the Hausdorff metric on the space of nonempty compact subsets of R and several fundamental analytical characteristics including convexity, boundedness and continuity are preserved under Katugampola fractional integration. Furthermore, we establish that both bounded variation and Lipschitz regularity of a set-valued mapping are preserved under its Katugampola fractional integral. We investigate the existence of regular selections associated with the Katugampola fractional integral and show that whenever the original set valued mapping admits a selection with a specified regularity property, the corresponding Katugampola fractional integral does as well.
Comments14 pages
