一类(ρ,k,φ)-比例Hilfer分数阶演化方程温和解的存在性OA
Existence of mild solutions for a class of(ρ,k,φ)-proportional Hilfer fractional evolution equation
在最新引入的(ρ,k,φ)-比例分数阶算子基础上,研究了一类(ρ,k,φ)-比例Hilfer分数阶Cauchy问题温和解的存在唯一性和解的连续依赖性.利用概率密度函数、(ρ,k,φ)-比例Hilfer分数阶导数的性质和半群理论,得到了温和解的定义.通过构造合适的加权空间,根据Banach压缩映射原理,研究了解的存在唯一性.构造广义Gronwall不等式,得到了解的连续依赖性.
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.
王海华;封全喜;赵婕
琼台师范学院 理学院,海口 海南 570100桂林理工大学 数学与统计学院,桂林 广西 541006琼台师范学院 理学院,海口 海南 570100
数理科学
分数阶导数存在性温和解连续依赖
fractional derivativeexistencemild solutionscontinuous dependence
《信阳师范大学学报（自然科学版）》 2026 (1)
94-100,7
国家自然科学基金项目(62166015)海南省自然科学基金项目(122MS088)
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