On fractional Langevin equation involving two fractional orders in different intervals

被引：35

作者：

Baghani, Hamid ^{[1
]}

Nieto, Juan J. ^{[2
]}

机构：

[1] Univ Sistan & Baluchestan, Fac Math Stat & Comp Sci, Dept Math, Zahedan, Iran

[2] Univ Santiago de Compostela, Inst Math, Dept Math Anal, Santiago De Compostela 15782, Spain

来源：

NONLINEAR ANALYSIS-MODELLING AND CONTROL | 2019年 / 24卷 / 06期

关键词：

Caputo fractional derivative; initial boundary conditions; existence and uniqueness; fractional Langevin equation; INITIAL-VALUE PROBLEMS; EXISTENCE; UNIQUENESS; MAPPINGS;

D O I：

10.15388/NA.2019.6.3

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we study a nonlinear Langevin equation involving two fractional orders alpha is an element of (0; 1] and beta is an element of (1; 2] with initial conditions. By means of an interesting fixed point theorem, we establish sufficient conditions for the existence and uniqueness of solutions for the fractional equations. Some illustrative numerical examples are also discussed.

引用

页码：884 / 897

页数：14

共 34 条

[1] On Riemann-Liouville fractional q-difference equations and their application to retarded logistic type model
Abdeljawad, Thabet
Alzabut, Jehad
[J]. MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2018, 41 (18) : 8953 - 8962
[2] A generalized q-fractional Gronwall inequality and its applications to nonlinear delay q-fractional difference systems
Abdeljawad, Thabet
Alzabut, Jehad
Baleanu, Dumitru
[J]. JOURNAL OF INEQUALITIES AND APPLICATIONS, 2016,
[3] A Survey on Existence Results for Boundary Value Problems of Nonlinear Fractional Differential Equations and Inclusions
Agarwal, Ravi P.
Benchohra, Mouffak
Hamani, Samira
[J]. ACTA APPLICANDAE MATHEMATICAE, 2010, 109 (03) : 973 - 1033
[4] A fixed point theorem for contraction type maps in partially ordered metric spaces and application to ordinary differential equations
Amini-Harandi, A.
Emami, H.
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2010, 72 (05) : 2238 - 2242
[5] [Anonymous], ANOMALOUS TRANSPORT
[6] Existence and uniqueness of solutions to fractional Langevin equations involving two fractional orders
Baghani, Hamid
[J]. JOURNAL OF FIXED POINT THEORY AND APPLICATIONS, 2018, 20 (02)
[7] A Fixed Point Theorem for a New Class of Set-Valued Mappings in R-Complete (Not Necessarily Complete) Metric Spaces
Baghani, Hamid
Ramezani, Maryam
[J]. FILOMAT, 2017, 31 (12) : 3875 - 3884
[8] On fractional Langevin equation involving two fractional orders
Baghani, Omid
[J]. COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2017, 42 : 675 - 681
[9] Coffey W.T., 2004, The Langevin Equation: With Applications to Stochastic Problems in Physics, Chemistry and Electrical Engineering
[10] Existence of solutions of initial value problems for nonlinear fractional differential equations
Deng, Jiqin
Deng, Ziming
[J]. APPLIED MATHEMATICS LETTERS, 2014, 32 : 6 - 12

← 1 2 3 4 →