A nonlinear fractional differential system : Existence and UHML-stability results
*Mohamed BezziouCorresponding authorm.bezziou@univ-dbkm.dzDepartment of MathematicsKhemis MilianaDjilali Bounaama UniversityAin Defla, 44000, Algeria0009-0009-2911-7003View full profile → , Zoubir Dahmanizzdahmani@yahoo.frLaboratory of Discrete and Applied Mathematics and Operations Research LAMDA-ROFaculty of SciencesUniversity of Blida 1Blida, 09000, Algeria0000-0003-4659-0723View full profile →
* Corresponding author · click or hover a name for details
- Received:
- 01 May 2025
- Published Online:
- 08 Jun 2026
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JIM-2405
- Pages:
- 1–18
Abstract
Keywords
Subject Classifications
References
[1] R.P. Agarwal, B. Kovacs and D. O’Regan, Existence of positive solution for a sixth-order differential system with variable parameters, J. Appl. Math. Comp, Vol. 44, pp. 437-454 (2014), https://doi:10.1007/s12190-013-0701-1.
[2] B. Baculková, New monotonicity properties and oscillation of n-order functional differential equations with deviating argument, Electron. J. Qual. Theory Differ. Equ, No. 30, pp. 1-10 (2023), https://doi.org/10.14232/ejqtde.2023.1.30.
[3] P. Baldwin, Asymptotic estimates of the eigenvalues of a sixth-order boundary-value problem obtained by using global phase-integral methods, Philos. Trans. Roy. Soc. London Ser. A, Vol. 322, No. 1566, pp. 281-305 (1987), https://doi.org/10.1098/rsta.1987.0051.
[4] Z. Bekkouche, H. Yfrah and Z. Dahmani, A study of coupled fractional differential system with nonlocal integral conditions: Existence and uniqueness, Ulam-Hyers stabilty, Journal of Interdisciplinary Mathematics, Vol. 28, No. 2, pp. 473-484 (2025), doi:10.47974/JIM-1784.
[5] K. Bensassa, Z. Dahmani and M. Z. Sarikaya, Solvability for a coupled system of 4-sequential fractional differential equations, Differ. Equ. & Appl, Vol. 2, No. 2, pp. 151-169 (2024), doi:10.7153/dea-2024-16-09.
[6] M. Bezziou, Z. Dahmani, I. Jebril and M.M. Belhamiti, Solvability for a differential system of Duffing type via Caputo-Hadamard approach, Appl. Math. Inf. Sci, Vol. 16, No. 2, pp. 341-352 (2022), doi:10.18576/amis/160222.
[7] M. Bezziou, Z. Dahmani, I. Jebril and M. Kaid, Caputo-Hadamard approach applications, solvability for an integro-differential problem of Lane-Emden type, J. Math. Comput. Sci, Vol. 11, No. 2, pp. 1629-1649 (2021), https://doi.org/10.28919/jmcs/5246.
[8] A.H. Bhrawy, Legendre-Galerkin method for sixth order boundary value problems, J. Egypt. Math. Soc, Vol. 17, No. 2, pp. 173-188 (2009).
[9] D. Bonanno and R. Livrea, A sequence of positive solutions for sixth-order ordinary nonlinear differential problems, Electron. J. Qual. Theory Differ. Equ, No. 20, pp. 1-17 (2021), https://doi.org/10.14232/ejqtde.2021.1.20.
[10] A. Boutayeb and E. Twizell, Numerical methods for the solution of special sixth-order boundary value problems, Int. J. Comput. Math, Vol. 45, pp. 207-223 (1992), https://doi.org/10.1080/00207169208804130.
[11] C.P. Danet, Existence and uniqueness for a semilinear sixth-order ODE, Electron, J. Qual. Theory Differ. Equ, No. 53, pp. 1-22 (2022), https://doi.org/10.14232/ejqtde.2022.1.53.
[12] L. D’Costa and N. Menaria, Fractional calculus of extended k-generalized Mittag-Leffler function and its properties, Journal of Interdisciplinary Mathematics, Vol. 27, No. 8, pp. 1741-1748 (2024), doi:10.47974/JIM-2036.
[13] L. Debnath, Recent applications of fractional calculus to science and engineering, Int. J. Math. Math. Sci, Vol. 54, pp. 3413-3442 (2003), https://doi.org/10.1155/S0161171203301486.
[14] Y. Gouari, Z. Dahmani and I. Jebril, Application of fractional calculus on a new differential problem of Duffing type, Adv. Math. Sci. J, Vol. 9, No. 12, pp. 10989-11002 (2020), https://doi.org/10.37418/amsj.9.12.
[15] Y. Gouari, Z. Dahmani and A. Ndiaye, A generalized sequential problem of Lane-Emden type via fractional calculus, Moroc. J. Pure Appl. Anal, Vol. 6, No. 2, pp. 168-183 (2020), doi:10.2478/mjpaa-2020-0013.
[16] Y. Gouari, M. Kaid and Z. Dahmani, Existence and uniqueness of solutions for fractional differential equations, (Under review).
[17] A. Granas and J. Dugundji, Fixed Point Theory, Springer, New York (2003).
[18] T. Gyulov, G. Morosanu and S. Tersian, Existence for a semilinear sixth-order ODE, J. Math. Anal. Appl, Vol. 321, pp. 86-98 (2006), https://doi.org/10.1016/j.jmaa.2005.08.007.
[19] M. Houas and M.E. Samei, Existence and Mittag-Leffler-Ulam-Stability results for Duffing type problem involving sequential fractional derivatives, Int. J. Appl. Comput. Math, Vol. 8, No. 185, pp. 1-24 (2022), https://doi.org/10.1007/s40819-022-01398-y.
[20] M. Kaid, M. Belhamiti, Z. Dahmani and A.T. Abdulrahman, Solvability for a system of fractional Sturm-Liouville Langevin equations, Sci. Int. (Lahore), Vol. 33, No. 1, pp. 75-89, (2021).
[21] A.A. Kilbas and S.A. Marzan, Nonlinear differential equation with the Caputo Fraction derivative in the space of continuously differentiable functions, Differ. Equ, Vol. 41, pp. 84-89 (2005), doi:10.1007/s10625-005-0137-y.
[22] A.A. Kilbas, H.M. Srivastava and J.J. Trujillo, Theory and applications of fractional differential equations, Elsevier Science B.V, (2006).
[23] V. Lakshmikantham and A.S. Vatsala, Basic theory of fractional differential equations, Nonlinear Anal, Vol. 69, pp. 2677-2682 (2008), https://doi.org/10.1142/10238.
[24] T. Li and G. Viglialoro, Boundedness for a nonlocal reaction chemotaxis model even in the attraction-dominated regime, Differ. Integral Equ, Vol. 34, pp. 315-336 (2021), doi:10.57262/die034-0506-315.
[25] W. Li, The existence and multiplicity of positive solutions of nonlinear sixth-order boundary value problem with three variable coefficients, Bound. Value Probl, Vol. 202, pp. 1-16 (2012), doi:10.1186/1687-2770-2012-22.
[26] W. Li, L. Zhang and Y. An, The existence of positive solutions for a nonlinear sixth-order boundary value problem, ISRN Appl. Math, Vol. 2012, Art. ID 926952, pp. 1-12 (2012), https://doi.org/10.5402/2012/926952.
[27] A.S. Nia, G.A. Afrouzi and H. Haghshenas, Existence and multiplicity results for sixth-order differential equations, Appl. Math. E-Notes, Vol. 24, pp. 512-519 (2024), http://www.math.nthu.edu.tw/ :amen/
[28] P.K. Pandy, A numerical method for the solution of fifth order boundary value problem in ordinary differential equations, Vladikavkaz Mathematical Journal, Vol. 19, No. 4, pp. 50-57 (2017), doi: 10.23671/VNC.2018.4.9167.
[29] S. Sharma and H. Nagar, The generalized Mittag-Leffler type function PkRq α,β,γ (z) associated with various new integral transforms, Journal of Interdisciplinary Mathematics, Vol. 27, No.8, pp.1805-1810 (2024), doi:10.47974/JIM-2044.
