Cauchy problem for non-autonomous fractional evolution equations

被引：3
|
作者：
He, Jia Wei [1 ]
Zhou, Yong [2 ,3 ]
机构：
[1] Guangxi Univ, Coll Math & Informat Sci, Nanning 530004, Peoples R China
[2] Xiangtan Univ, Fac Math & Computat Sci, Xiangtan 411105, Hunan, Peoples R China
[3] Macau Univ Sci & Technol, Sch Comp Sci & Engn, Macau 999078, Peoples R China
来源：
FRACTIONAL CALCULUS AND APPLIED ANALYSIS | 2022年 / 25卷 / 06期
关键词：
Fractional calculus; Non-autonomous evolution equations; Solvability; Mittag-Leffler functions; WELL-POSEDNESS; WAVE-EQUATIONS; TIME; DIFFUSION; REGULARITY; CALCULUS;
D O I：
10.1007/s13540-022-00094-4
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we study the solvability of Cauchy problem for a class of non-autonomous fractional evolution equation with Caputo's fractional derivative of order alpha is an element of (1, 2), which can be applied to model the time dependent coefficients fractional differential systems. We first introduce an operator family and analyze its properties, by the iterative method, we construct a solution to an operator-valued Volterra equation, which is the most critical ingredient to prove solvability of the problem. Finally, based on the solution operators we establish the existence and uniqueness of classical solutions.
引用
收藏
页码：2241 / 2274
页数：34
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