The Langevin Equation in Terms of Generalized Liouville-Caputo Derivatives with Nonlocal Boundary Conditions Involving a Generalized Fractional Integral

被引：31
|
作者：
Ahmad, Bashir [1 ]
Alghanmi, Madeaha [1 ]
Alsaedi, Ahmed [1 ]
Srivastava, Hari M. [2 ,3 ]
Ntouyas, Sotiris K. [1 ,4 ]
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 Victoria, Dept Math & Stat, Victoria, BC V8W 3R4, Canada
[3] China Med Univ, China Med Univ Hosp, Dept Med Res, Taichung 40402, Taiwan
[4] Univ Ioannina, Dept Math, Ioannina 45110, Greece
来源：
MATHEMATICS | 2019年 / 7卷 / 06期
关键词：
Langevin equation; generalized fractional integral; generalized Liouville-Caputo derivative; nonlocal boundary conditions; existence; fixed point;
D O I：
10.3390/math7060533
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we establish sufficient conditions for the existence of solutions for a nonlinear Langevin equation based on Liouville-Caputo-type generalized fractional differential operators of different orders, supplemented with nonlocal boundary conditions involving a generalized integral operator. The modern techniques of functional analysis are employed to obtain the desired results. The paper concludes with illustrative examples.
引用
收藏
页数：10
相关论文
共 50 条
  • [41] NONLINEAR SEQUENTIAL RIEMANN-LIOUVILLE AND CAPUTO FRACTIONAL DIFFERENTIAL EQUATIONS WITH NONLOCAL AND INTEGRAL BOUNDARY CONDITIONS
    Asawasamrit, Suphawat
    Phuangthong, Nawapol
    Ntouyas, Sotiris K.
    Tariboon, Jessada
    [J]. INTERNATIONAL JOURNAL OF ANALYSIS AND APPLICATIONS, 2019, 17 (01): : 47 - 63
  • [42] Hyers-Ulam Stability and Existence of Solutions to the Generalized Liouville-Caputo Fractional Differential Equations
    Liu, Kui
    Feckan, Michal
    Wang, Jinrong
    [J]. SYMMETRY-BASEL, 2020, 12 (06):
  • [43] Existence results for fractional order differential equation with nonlocal Erdélyi–Kober and generalized Riemann–Liouville type integral boundary conditions at resonance
    Qiao Sun
    Shuman Meng
    Yujun Cui
    [J]. Advances in Difference Equations, 2018
  • [44] Generalized Sturm-Liouville and Langevin equations via Hadamard fractional derivatives with anti-periodic boundary conditions
    Kiataramkul, Chanakarn
    Ntouyas, Sotiris K.
    Tariboon, Jessada
    Kijjathanakorn, Atthapol
    [J]. BOUNDARY VALUE PROBLEMS, 2016,
  • [45] Generalized Sturm-Liouville and Langevin equations via Hadamard fractional derivatives with anti-periodic boundary conditions
    Chanakarn Kiataramkul
    Sotiris K Ntouyas
    Jessada Tariboon
    Atthapol Kijjathanakorn
    [J]. Boundary Value Problems, 2016
  • [46] On Some Inequalities Involving Liouville-Caputo Fractional Derivatives and Applications to Special Means of Real Numbers
    Samet, Bessem
    Aydi, Hassen
    [J]. MATHEMATICS, 2018, 6 (10)
  • [47] Existence Results for Sequential Riemann-Liouville and Caputo Fractional Differential Inclusions with Generalized Fractional Integral Conditions
    Tariboon, Jessada
    Ntouyas, Sotiris K.
    Ahmad, Bashir
    Alsaedi, Ahmed
    [J]. MATHEMATICS, 2020, 8 (06)
  • [48] Solvability of a generalized Ψ-Riemann-Liouville fractional BVP under nonlocal boundary conditions
    Haddouchi, Faouzi
    Samei, Mohammad Esmael
    [J]. MATHEMATICS AND COMPUTERS IN SIMULATION, 2024, 219 : 355 - 377
  • [49] Analysis of Caputo Sequential Fractional Differential Equations with Generalized Riemann-Liouville Boundary Conditions
    Gunasekaran, Nallappan
    Manigandan, Murugesan
    Vinoth, Seralan
    Vadivel, Rajarathinam
    [J]. FRACTAL AND FRACTIONAL, 2024, 8 (08)
  • [50] Fractional order differential systems involving right Caputo and left Riemann–Liouville fractional derivatives with nonlocal coupled conditions
    Bashir Ahmad
    Sotiris K. Ntouyas
    Ahmed Alsaedi
    [J]. Boundary Value Problems, 2019
12345