Analytical solutions to fractional evolution equations with almost sectorial operators

被引：17

作者：

Ding, Xiao-Li ^{[1
]}

Ahmad, Bashir ^{[2
]}

机构：

[1] Xian Polytech Univ, Dept Math, Xian 710048, Shaanxi, Peoples R China

[2] King Abdulaziz Univ, Fac Sci, Nonlinear Anal & Appl Math NAAM Res Grp, POB 80203, Jeddah 21589, Saudi Arabia

来源：

ADVANCES IN DIFFERENCE EQUATIONS | 2016年

关键词：

fractional neutral evolution equations; almost sectorial operators; fixed point theorems; existence and uniqueness; mild solutions; strong solutions and classical solutions; FUNCTIONAL-DIFFERENTIAL EQUATIONS; EXISTENCE; DYNAMICS; CONTINUITY; INCLUSIONS; UNIQUENESS;

D O I：

10.1186/s13662-016-0927-y

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, with the aid of functional analysis, for almost sectorial operators and some fixed point theorems, we study the existence and uniqueness of mild solutions to fractional neutral evolution equations with almost sectorial operators. We also show that mild solutions can become strong and classical solutions under appropriate assumptions. Finally, we present an example to illustrate the applicability of our results.

引用

页数：25

共 44 条

[21] Darwish MA, 2010, J CONVEX ANAL, V17, P413
[22] On initial and boundary value problems for fractional order mixed type functional differential inclusions
Darwish, Mohamed Abdalla
Ntouyas, S. K.
[J]. COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2010, 59 (03) : 1253 - 1265
[23] Darwish MA, 2009, DYNAM SYST APPL, V18, P539
[24] Analysis of fractional differential equations
Diethelm, K
Ford, NJ
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2002, 265 (02) : 229 - 248
[25] ANALYTICAL SOLUTIONS FOR THE MULTI-TERM TIME-SPACE FRACTIONAL REACTION-DIFFUSION EQUATIONS ON AN INFINITE DOMAIN
Ding, Xiao-Li
Nieto, Juan J.
[J]. FRACTIONAL CALCULUS AND APPLIED ANALYSIS, 2015, 18 (03) : 697 - 716
[26] Integrated semigroups and parabolic equations. Part I: linear perburbation of almost sectorial operators
Ducrot, Arnaud
Magal, Pierre
Prevost, Kevin
[J]. JOURNAL OF EVOLUTION EQUATIONS, 2010, 10 (02) : 263 - 291
[27] Henry D., 1981, LECT NOTES MATH
[28] Hernández E, 2011, DIFFER EQUAT APPL, V3, P1
[29] Remarks on fractional derivatives
Li, Changpin
Deng, Weihua
[J]. APPLIED MATHEMATICS AND COMPUTATION, 2007, 187 (02) : 777 - 784
[30] Mild solutions for abstract fractional differential equations with almost sectorial operators and infinite delay
Li, Fang
[J]. ADVANCES IN DIFFERENCE EQUATIONS, 2013,

← 1 2 3 4 5 →