Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
권호 표지
DOI QR코드

DOI QR Code

Existence and Uniqueness Results for a Coupled System of Nonlinear Fractional Langevin Equations

  • Sushma Basil (Department of Mathematics, PSGR Krishnammal College for Women) ;
  • Santhi Antony (Department of Applied Mathematics and Computational Sciences, PSG College of Technology) ;
  • Muralisankar Subramanian (School of Mathematics, Madurai Kamaraj University)
  • Received : 2022.08.29
  • Accepted : 2023.09.04
  • Published : 2023.09.30
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper, we present a sufficient condition for the unique existence of solutions for a coupled system of nonlinear fractional Langevin equations with a new class of multipoint and nonlocal integral boundary conditions. We define a 𝓩*λ-contraction mapping and present the sufficient condition by identifying the problem with an equivalent fixed point problem in the context of b-metric spaces. Finally, some numerical examples are given to validate our main results.

Keywords

References

  1. H. Baghani, J. Alzabut and J. J. Nieto, A coupled System of Langevin Differential Equations of Fractional Order and Associated to Antiperiodic Boundary Conditions, Math Meth Appl Sci., (2020), 1-11.
  2. I. A. Bakhtin, The Contraction Mapping Principle in Quasi Metric Spaces, Funct. Anal. Unianowsk Gos. Ped. Inst., 30(1989), 26-37.
  3. T. G. Bhaskar and V. Lakshmikantham, Fixed Point Theorems in Partially Ordered Metric Spaces and Applications, Nonlinear Analysis, 65(7)(2006), 1379-1393. https://doi.org/10.1016/j.na.2005.10.017
  4. R. Darzi, B. Agheli and J. J. Nieto, Langevin Equation Involving Three Fractional Orders, J. Stat. Phys., 178(2020), 986-995. https://doi.org/10.1007/s10955-019-02476-0
  5. H. Fazli, H. G. Sun and J. J. Nieto, Fractional Langevin Equation Involving Two Fractional Orders: Existence and Uniqueness Revisited, Mathematics, 8(5)(2020), 1-10. https://doi.org/10.3390/math8050743
  6. F. Khojasteh, S. Shukla and S. Radenovic, A New Approach to the Study of Fixed Point Theory for Simulation Functions, Filomat, 29(6)(2015), 1189-1194. https://doi.org/10.2298/FIL1506189K
  7. R. Kubo, The fluctuation-dissipation theorem, Rep. Prog. Phys., 29(1966), 255-284. https://doi.org/10.1088/0034-4885/29/1/306
  8. P. Langevin, On the theory of Brownian motion, Comptes Rendus, 146(1908), 530-533.
  9. A. K. Mirmostafaee, Coupled Fixed Points for Mappings on a b-metric space with a Graph, Mathematicki Vesnik, 69(3)(2017), 214-225.
  10. A. Salem, F. Alzahrani and M. Alnegga, Coupled System of Nonlinear Fractional Langevian Equation with Multipoint and Nonlocal Integral Boundary Conditions, Mathematical Problems in Engineering, (2020), 1-15.
  11. A. Santhi, S. Muralisankar and R. P. Agarwal, A New Coupled Fixed Point Theorem via Simulation Function with Application, Matematicki Vesnik, 73(3)(2021), 209-222.
  12. W. Sintunavarat, P. Kumam and Y. J. Cho, Coupled Fixed Point Theorems for Nonlinear Contractions without Mixed Monotone Property, Fixed Point Theory Appl., 170(2012), 1-12. https://doi.org/10.1186/1687-1812-2012-170
  13. T. Yu and M. Luo, Existence and Uniqueness of Solutions of Initial Value Problems for Nonlinear Langevin Equation Involving Two Fractional Orders, Commun. Nonlinear. Sci. Numer. Simulat., 19(2014), 1661-1668. https://doi.org/10.1016/j.cnsns.2013.09.035
  14. B. Zlatanov, A Variational Principle and Coupled Fixed Points, J. Fixed Point Theory Appl., 21(69)(2019), 1-13. https://doi.org/10.1007/s11784-018-0638-y
  15. H. Zhou, J. Alzabut and L. Yang, On fractional Langevin differential equations with anti-periodic boundary conditions, Eur. Phys. J. Spec. Topics., 226(2017), 3577-3590. https://doi.org/10.1140/epjst/e2018-00082-0