EXISTENCE AND UNIQUENESS OF SOLUTIONS OF THE FRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS IN VECTOR-VALUED FUNCTION SPACE

被引：0
|
作者：
Rachid, Bahloul [1 ]
机构：
[1] Fac Sci & Technol, BP 2202, Fes, Morocco
来源：
ARCHIVUM MATHEMATICUM | 2019年 / 55卷 / 02期
关键词：
periodic solution; L-p-multipliers; UMD-spaces; FOURIER MULTIPLIER THEOREMS; PERIODIC-SOLUTIONS; INFINITE DELAY; MAXIMAL REGULARITY;
D O I：
10.5817/AM2019-2-97
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The aim of this work is to study the existence and uniqueness of solutions of the fractional integro-differential equations d/dt[x(t) - L(x(t))] = A[x(t) - L(x(t))] + G(x(t)) + + 1/Gamma(alpha) integral(t)(-infinity)(t - s)(alpha-1)(integral(s)(-infinity) a(s -xi )x(xi)d xi)ds + f(t), (alpha > 0) with the periodic condition x(0) = x(2 pi), where a is an element of L-1 (R+). Our approach is based on the R-boundedness of linear operators L-p-multipliers and UMD-spaces.
引用
收藏
页码：97 / 108
页数：12
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