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 50 条

[41] ON THE NONLINEAR GENERALIZED LANGEVIN EQUATION INVOLVING ψ-CAPUTO FRACTIONAL DERIVATIVES
Nguyen Minh Dien
Dang Duc Trong
FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY, 2021, 29 (06)
[42] A COUPLED SYSTEM OF NONLINEAR LANGEVIN FRACTIONAL q-DIFFERENCE EQUATIONS ASSOCIATED WITH TWO DIFFERENT FRACTIONAL ORDERS IN BANACH SPACE
Boutiara, Abdellatif
KRAGUJEVAC JOURNAL OF MATHEMATICS, 2024, 48 (04): : 555 - 575
[43] Nonlinear fractional differential equation involving two mixed fractional orders with nonlocal boundary conditions and Ulam–Hyers stability
Fang Li
Wenjing Yang
Huiwen Wang
Boundary Value Problems, 2020
[44] Multi-Point and Anti-Periodic Conditions for Generalized Langevin Equation with Two Fractional Orders
Salem, Ahmed
Alghamdi, Balqees
FRACTAL AND FRACTIONAL, 2019, 3 (04) : 1 - 14
[45] Differentiation to fractional orders and the fractional telegraph equation
Camargo, R. Figueiredo
Chiacchio, Ary O.
de Oliveira, E. Capelas
JOURNAL OF MATHEMATICAL PHYSICS, 2008, 49 (03)
[46] On a viscoelastic rod with constitutive equation containing fractional derivatives of two different orders
Stankovic, B
Atanackovic, TM
MATHEMATICS AND MECHANICS OF SOLIDS, 2004, 9 (06) : 629 - 656
[47] Applications of the Mittag–Leffler function in solvability and stability of a class of fractional Langevin equations with two fractional orders
Hamid Baghani
Juan J. Nieto
The Journal of Analysis, 2024, 32 : 915 - 929
[48] Nonlinear fractional differential equation involving two mixed fractional orders with nonlocal boundary conditions and Ulam-Hyers stability
Li, Fang
Yang, Wenjing
Wang, Huiwen
BOUNDARY VALUE PROBLEMS, 2020, 2020 (01)
[49] On nonlocal integral and derivative boundary value problem of nonlinear Hadamard Langevin equation with three different fractional orders
Berhail, Amel
Tabouche, Nora
Matar, Mohammed M.
Alzabut, Jehad
BOLETIN DE LA SOCIEDAD MATEMATICA MEXICANA, 2020, 26 (02): : 303 - 318
[50] TWO FRACTIONAL ORDER LANGEVIN EQUATION WITH NEW CHAOTIC DYNAMICS
Belhamiti, Meriem Mansouria
Dahmani, Zoubir
Sarikaya, Mehmet Zeki
COMMUNICATIONS FACULTY OF SCIENCES UNIVERSITY OF ANKARA-SERIES A1 MATHEMATICS AND STATISTICS, 2023, 72 (03): : 663 - 685

← 1 2 3 4 5 →