International Journal of Differential Equations

Existence Results for a System of Coupled Hybrid Differential Equations with Fractional Order

Mohamed Hannabou and Khalid Hilal

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

This paper studies the existence of solutions for a system of coupled hybrid fractional differential equations. We make use of the standard tools of the fixed point theory to establish the main results. The existence and uniqueness result is elaborated with the aid of an example.

Article information

Source
Int. J. Differ. Equ., Volume 2020 (2020), Article ID 3038427, 8 pages.

Dates
Received: 24 November 2019
Accepted: 18 January 2020
First available in Project Euclid: 14 May 2020

Permanent link to this document
https://projecteuclid.org/euclid.ijde/1589421701

Digital Object Identifier
doi:10.1155/2020/3038427

Mathematical Reviews number (MathSciNet)
MR4087062

Citation

Hannabou, Mohamed; Hilal, Khalid. Existence Results for a System of Coupled Hybrid Differential Equations with Fractional Order. Int. J. Differ. Equ. 2020 (2020), Article ID 3038427, 8 pages. doi:10.1155/2020/3038427. https://projecteuclid.org/euclid.ijde/1589421701


Export citation

References

  • B. Ahmad and J. J. Nieto, “Existence results for a coupled system of nonlinear fractional differential equations with three-point boundary conditions,” Computers & Mathematics with Applications, vol. 58, no. 9, pp. 1838–1843, 2009.
  • B. Ahmad and S. K. Ntouyas, “A four-point nonlocal integral boundary value problem for fractional differential equations of arbitrary order,” Electronic Journal of Qualitative Theory of Differential Equations, vol. 22, p. 15, 2011.
  • B. Ahmad, S. K. Ntouyas, and A. Alsaedi, “New existence results for nonlinear fractional differential equations with threepoint integral boundary conditions,” Advances in Difference Equations, vol. 2011, Article ID 107384, p. 11, 2011.
  • B. Ahmad, J. J. Nieto, and J. Pimentel, “Some boundary value problems of fractional differential equations and inclusions,” Computers & Mathematics with Applications, vol. 62, no. 3, pp. 1238–1250, 2011.
  • B. Ahmad and S. K. Ntouyas, “An existence theorem for fractional hybrid differential inclusions of HADamard type with DIRichlet boundary conditions,” Abstract and Applied Analysis, vol. 2014, Article ID 705809, 7 pages, 2014.
  • J. Sabatier, O. P. Agrawal, and J. A. T. Machado, Advances in Fractional Calculus: Theoretical Developments and Applications in Physics and Engineering, Springer, Dordrecht, Netherlands, 2007.
  • B. Ahmad and S. K. Ntouyas, “A fully Hadamard type integral boundary value problem of a coupled system of fractional differential equations,” Fractional Calculus and Applied Analysis, vol. 17, no. 2, pp. 348–360, 2014.
  • S. Melliani, K. Hilal, and M. Hannabou, “Existence results of hybrid fractional integro-differential equations: theoretical aspects and applications,” in Recent Advances in Intuitionistic Fuzzy Logic Systems, vol. 372, Springer, Berlin, Germany, 2019, Studies in Fuzziness and Soft Computing.
  • X. Liu, Z. Liu, and X. Fu, “Relaxation in nonconvex optimal control problems described by fractional differential equations,” Journal of Mathematical Analysis and Applications, vol. 409, no. 1, pp. 446–458, 2014.
  • J. R. Graef, L. Kong, and M. Wang, “Existence and uniqueness of solutions for a fractional boundary value problem on a graph,” Fractional Calculus and Applied Analysis, vol. 17, no. 2, pp. 499–510, 2014.
  • F. Punzo and G. Terrone, “On the cauchy problem for a general fractional porous medium equation with variable density,” Nonlinear Analysis: Theory, Methods & Applications, vol. 98, pp. 27–47, 2014.
  • K. Razminia, A. Razminia, and J. A. Tenreiro Machado, “Analysis of diffusion process in fractured reservoirs using fractional derivative approach,” Communications in Nonlinear Science and Numerical Simulation, vol. 19, no. 9, pp. 3161–3170, 2014.
  • D. Baleanu and P. Agarwal, “Certain inequalities involving the fractional q-integral operators,” Abstract and Applied Analysis, vol. 2014, Article ID 371274, 10 pages, 2014.
  • S. K. Ntouyas and M. Obaid, “A coupled system of fractional differential equations with nonlocal integral boundary conditions,” Advances in Difference Equations, vol. 2012, no. 1, 2012.
  • Z. Hu and W. Liu, “Solvability of a coupled system of fractional differential equations with periodic boundary conditions at resonance,” Ukrainian Mathematical Journal, vol. 65, no. 11, pp. 1619–1633, 2014.
  • S. Sun, Y. Zhao, Z. Han, and Y. Li, “The existence of solutions for boundary value problem of fractional hybrid differential equations,” Communications in Nonlinear Science and Numerical Simulation, vol. 17, no. 12, pp. 4961–4967, 2012.
  • A. Granas and J. Dugundji, Fixed Point Theory, Springer, New York, NY, USA, 2003. \endinput