A Cauchy problem for fractional evolution equations with Hilfer’s fractional derivative on semi-infinite interval

被引：0
作者：
Yong Zhou
Jia Wei He
机构：
[1] Xiangtan University,Faculty of Mathematics and Computational Science
[2] King Abdulaziz University,Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Faculty of Science
[3] Guangxi University,College of Mathematics and Information Science
来源：
Fractional Calculus and Applied Analysis | 2022年 / 25卷
关键词：
Hilfer’s fractional derivative; Existence; Semi-infinite interval; 26A33 (Primary); 34A12;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In this paper, we consider a Cauchy problem for fractional evolution equations with Hilfer’s fractional derivative on semi-infinite interval. An elementary fact shows that semi-infinite interval is not compact, the classical Ascoli-Arzelà theorem is not valid. In order to establish the global existence criteria, we first generalize Ascoli-Arzelà theorem into the semi-infinite interval. Next, we introduce a new concept of mild solutions based on cosine/sine family and probability density function and obtain several existence results of mild solutions on semi-infinite interval.
引用
收藏
页码：924 / 961
页数：37
相关论文
共 51 条
[1]  
Bazhlekova E(2012)Existence and uniqueness results for a fractional evolution equation in Hilbert space Fract. Calc. Appl. Anal. 15 232-243
[2]  
Furati KM(2012)Existence and uniqueness for a problem involving Hilfer fractional derivative Comput. Math. Appl. 64 1616-1626
[3]  
Kassim MD(2012)Structure of the solution set to impulsive functional differential inclusions on the half-line Nonlinear Differ. Equ. Appl. 19 609-627
[4]  
Tatar Ne-(2022)On well-posedness of semilinear Rayleigh-Stokes problem with fractional derivative on Adv. Nonlinear Anal. 11 580-597
[5]  
Gabor G(2002)Experimental evidence for fractional time evolution in glass forming materials Chemical Physics 284 399-408
[6]  
Grudzka A(2009)Operational method for the solution of fractional differential equations with generalized Riemann-Liouville fractional derivatives Fract. Calc. Appl. Anal. 12 299-318
[7]  
He JW(2011)Existence of solutions of initial problems for nonlinear fractional differential equations on the half-axis Nonlinear Anal. 74 5975-5986
[8]  
Zhou Y(2010)Mild solutions of semilinear evolution equation on an unbounded interval and their applications Nonlinear Anal. 72 2119-2126
[9]  
Peng L(2016)Fractional abstract Cauchy problem with order Dyn. Partial Differ. Equ. 13 155-177
[10]  
Ahmad B(2008)The criterion of relative compactness for a class of abstract function groups in an infinite interval and its applications J. Sys. Sci. & Math. Scis. 28 370-378
123456