Mild solutions of Riemann-Liouville fractional differential equations with fractional impulses

被引：8

作者：

Anguraj, Annamalai ^{[1
]}

Kanjanadevi, Subramaniam ^{[1
]}

Jose Nieto, Juan ^{[2
,3
]}

机构：

[1] PSG Coll Arts & Sci, Dept Math, Coimbatore 641014, Tamil Nadu, India

[2] King Abdulaziz Univ, Dept Math, Fac Sci, Jeddah 21589, Saudi Arabia

[3] Univ Santiago de Compostela, Dept Math Anal, Fac Math, Santiago De Compostela 15782, Spain

来源：

NONLINEAR ANALYSIS-MODELLING AND CONTROL | 2017年 / 22卷 / 06期

关键词：

fractional derivative; fractional impulsive conditions; (a; k)-regularized resolvent operator; Riemann-Liouville operator; INITIAL-VALUE PROBLEMS; EVOLUTION-EQUATIONS; EXISTENCE; DERIVATIVES;

D O I：

10.15388/NA.2017.6.2

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider Riemann-Liouville fractional differential equations with fractional-order derivative in the impulsive conditions. We study the existence of the mild solution by applying the Laplace transform method and (a, k)-regularized resolvent operator. We use the contraction mapping principle and fixed point theorem for condensing map to prove our existence results.

引用

页码：753 / 764

页数：12

共 50 条

[1] EXACT SOLUTIONS OF LINEAR RIEMANN-LIOUVILLE FRACTIONAL DIFFERENTIAL EQUATIONS WITH IMPULSES
Agarwal, Ravi P.
Hristova, Snezhana
O'Regan, Donal
[J]. ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, 2020, 50 (03) : 779 - 791
[2] Attractivity of solutions of Riemann-Liouville fractional differential equations
Zhu, Tao
[J]. ELECTRONIC JOURNAL OF QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS, 2022, (52) : 1 - 12
[3] Fuzzy differential equations with Riemann-Liouville generalized fractional integrable impulses
Truong Vinh An
Ngo Van Hoa
[J]. FUZZY SETS AND SYSTEMS, 2022, 429 : 74 - 100
[4] RIEMANN-LIOUVILLE FRACTIONAL DIFFERENTIAL EQUATIONS WITH FRACTIONAL BOUNDARY CONDITIONS
Ahmad, Bashir
Nieto, Juan J.
[J]. FIXED POINT THEORY, 2012, 13 (02): : 329 - 336
[5] Existence of Solutions for Fractional Differential Equations Involving Two Riemann-Liouville Fractional Orders
Mohamed Houas
[J]. Analysis in Theory and Applications, 2018, 34 (03) : 253 - 274
[6] The Multiplicity Solutions for Nonlinear Fractional Differential Equations of Riemann-Liouville Type
Tianfu Ma
Baoqiang Yan
[J]. Fractional Calculus and Applied Analysis, 2018, 21 : 801 - 818
[7] THE MULTIPLICITY SOLUTIONS FOR NONLINEAR FRACTIONAL DIFFERENTIAL EQUATIONS OF RIEMANN-LIOUVILLE TYPE
Ma, Tianfu
Yan, Baoqiang
[J]. FRACTIONAL CALCULUS AND APPLIED ANALYSIS, 2018, 21 (03) : 801 - 818
[8] Basic Concepts of Riemann-Liouville Fractional Differential Equations with Non-Instantaneous Impulses
Agarwal, Ravi
Hristova, Snezhana
O'Regan, Donal
[J]. SYMMETRY-BASEL, 2019, 11 (05):
[9] Existence and Integral Representation of Scalar Riemann-Liouville Fractional Differential Equations with Delays and Impulses
Agarwal, Ravi
Hristova, Snezhana
O'Regan, Donal
[J]. MATHEMATICS, 2020, 8 (04)
[10] Cauchy problems for fractional differential equations with Riemann-Liouville fractional derivatives
Li Kexue
Peng Jigen
Jia Junxiong
[J]. JOURNAL OF FUNCTIONAL ANALYSIS, 2012, 263 (02) : 476 - 510

← 1 2 3 4 5 →