Nonlinear Langevin equations and inclusions involving mixed fractional order derivatives and variable coefficient with fractional nonlocal-terminal conditions

被引：12
|
作者：
Ahmad, Bashir [1 ]
Alsaedi, Ahmed [1 ]
Ntouyas, Sotiris K. [1 ,2 ]
机构：
[1] King Abdulaziz Univ, Fac Sci, Dept Math, Nonlinear Anal & Appl Math NAAM Res Grp, POB 80203, Jeddah 21589, Saudi Arabia
[2] Univ Ioannina, Dept Math, Ioannina 45110, Greece
来源：
AIMS MATHEMATICS | 2019年 / 4卷 / 03期
关键词：
fractional derivatives; fractional integral; Langevin equations; nonlocal terminal value problems; existence; uniqueness; fixed point theorems; DIFFERENTIAL-EQUATIONS; EXISTENCE;
D O I：
10.3934/math.2019.3.626
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we discuss the existence and uniqueness of solutions for a new kind of Langevin equation involving Riemann-Liouville as well as Caputo fractional derivatives, and variable coefficient, supplemented with nonlocal-terminal fractional integro-differential conditions. The proposed study is based on modem tools of functional analysis. We also extend our discussion to the associated inclusions problem. For the applicability of the obtained results, several examples are constructed. Some interesting observations are also presented.
引用
收藏
页码：626 / 647
页数：22
相关论文
共 50 条
  • [21] Analysis of a Coupled System of Nonlinear Fractional Langevin Equations with Certain Nonlocal and Nonseparated Boundary Conditions
    Laadjal, Zaid
    Al-Mdallal, Qasem M.
    Jarad, Fahd
    JOURNAL OF MATHEMATICS, 2021, 2021
  • [22] On system of nonlinear coupled differential equations and inclusions involving Caputo-type sequential derivatives of fractional order
    Subramanian, M.
    Manigandan, M.
    Tunc, C.
    Gopal, T. N.
    Alzabut, J.
    JOURNAL OF TAIBAH UNIVERSITY FOR SCIENCE, 2022, 16 (01): : 1 - 23
  • [23] Fractional Retarded Differential Equations Involving Mixed Nonlocal Plus Local Initial Conditions
    Zhang, Xuping
    Chen, Pengyu
    Li, Yongxiang
    NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, 2019, 40 (14) : 1678 - 1702
  • [24] Nonlinear differential equations involving mixed fractional derivatives with functional boundary data
    Zhang, Shuqin
    Sun, Bingzhi
    MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2022, 45 (10) : 5930 - 5944
  • [25] Nonlinear Degenerate Fractional Evolution Equations with Nonlocal Conditions
    Derdar, Nedjemeddine
    Debbouche, Amar
    FUNDAMENTA INFORMATICAE, 2017, 151 (1-4) : 473 - 485
  • [26] Nonlinear Integro-Differential Equations Involving Mixed Right and Left Fractional Derivatives and Integrals with Nonlocal Boundary Data
    Ahmad, Bashir
    Broom, Abrar
    Alsaedi, Ahmed
    Ntouyas, Sotiris K.
    MATHEMATICS, 2020, 8 (03)
  • [27] A study of coupled systems of mixed order fractional differential equations and inclusions with coupled integral fractional boundary conditions
    Ntouyas, Sotiris K.
    Al-Sulami, Hamed H.
    ADVANCES IN DIFFERENCE EQUATIONS, 2020, 2020 (01)
  • [28] A study of coupled systems of mixed order fractional differential equations and inclusions with coupled integral fractional boundary conditions
    Sotiris K. Ntouyas
    Hamed H. Al-Sulami
    Advances in Difference Equations, 2020
  • [29] 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
  • [30] Fractional order differential systems involving right Caputo and left Riemann–Liouville fractional derivatives with nonlocal coupled conditions
    Bashir Ahmad
    Sotiris K. Ntouyas
    Ahmed Alsaedi
    Boundary Value Problems, 2019
12345