信阳师范大学学报（自然科学版）2026，Vol.39Issue(1)：94-100,7.DOI:10.3969/j.issn.2097-583X.2026.01.013
一类(ρ,k,φ)-比例Hilfer分数阶演化方程温和解的存在性
Existence of mild solutions for a class of(ρ,k,φ)-proportional Hilfer fractional evolution equation
摘要
Abstract
The existence,uniqueness and continuous dependence of solutions for a class of(ρ,k,φ)-proportional Hilfer fractional Cauchy problems were investigated.The probability density function,properties of the(ρ,k,φ)-proportional Hilfer fractional derivative and semigroup theory were utilized to define mild solutions.A proper weighted space was introduced,and within this space,the Banach contraction principle was applied to discuss the uniqueness of the solutions.The continuous dependence of the data on the Cauchy problem was proven by constructing a generalized Gronwall inequality.关键词
分数阶导数/存在性/温和解/连续依赖Key words
fractional derivative/existence/mild solutions/continuous dependence分类
数理科学引用本文复制引用
王海华,封全喜,赵婕..一类(ρ,k,φ)-比例Hilfer分数阶演化方程温和解的存在性[J].信阳师范大学学报（自然科学版）,2026,39(1):94-100,7.基金项目
国家自然科学基金项目(62166015) （62166015）
海南省自然科学基金项目(122MS088) （122MS088）
