Publication Cover
Mathematical and Computer Modelling of Dynamical Systems
Methods, Tools and Applications in Engineering and Related Sciences
Volume 30, 2024 - Issue 1
324
Views
0
CrossRef citations to date
0
Altmetric
Research Article

Analytical and approximate monotone solutions of the mixed order fractional nabla operators subject to bounded conditions

, , , , &
Pages 626-639 | Received 18 Mar 2024, Accepted 04 Jun 2024, Published online: 05 Jul 2024

References

  • Abdeljawad T. 2018. Different type kernel h–fractional differences and their fractional h–sums. Chaos Solit Fract. 116:146–156. doi: 10.1016/j.chaos.2018.09.022.
  • Abdeljawad T, Baleanu D. 2016. Discrete fractional differences with nonsingular discrete Mittag-Leffler kernels. Adv Differ Equ. 2016(1):1–5. doi: 10.1186/s13662-016-0949-5.
  • Atici FM, Eloe PW. 2008. Initial value problems in discrete fractional calculus. Proc Amer Math Soc. 137(3):981–989. doi: 10.1090/S0002-9939-08-09626-3.
  • Baleanu D, Wu GC, Bai YR, Chen FL. 2017. Stability analysis of Caputo-like discrete fractional systems. Commun Nonlinear Sci Numer Simul. 48:520–530. doi: 10.1016/j.cnsns.2017.01.002.
  • Dahal R, Goodrich CS, Lyons B. 2021. Monotonicity results for sequential fractional differences of mixed orders with negative lower bound. J Differ Equ Appl. 27(11):1574–1593. doi: 10.1080/10236198.2021.1999434.
  • Gholami Y, Ghanbari K. 2016. Coupled systems of fractional ∇-difference boundary value problems. Differ Eq Appl. 8(4):459–470. doi: 10.7153/dea-08-26.
  • Goodrich CS, Jonnalagadda JM. 2021. Monotonicity results for CFC nabla fractional differences with negative lower bound. Anal (Berlin). 41(4):221–229. doi: 10.1515/anly-2021-0011.
  • Goodrich CS, Lyons B. 2020. Positivity and monotonicity results for triple sequential fractional differences via convolution. Analysis. 40(2):89–103. doi: 10.1515/anly-2019-0050.
  • Goodrich CS, Peterson AC. 2015. Discrete fractional calculus. (NY): Springer.
  • Liu X, Du F, Anderson D, Jia B. 2020. Monotonicity results for nabla fractional h-difference operators. Math Meth Appl Sci. 1–21. doi: 10.1002/mma.6823.
  • Mohammed PO. 2024. Some positive results for exponential-kernel difference operators of Riemann-Liouville type. Math Model Control. 4(1):133–140. doi: 10.3934/mmc.2024012.
  • Mohammed PO, Abdeljawad T. 2023. Discrete generalized fractional operators defined using h-discrete Mittag-Leffler kernels and applications to AB fractional difference systems. Math Meth Appl Sci. 46(7):7688–7713. doi: 10.1002/mma.7083.
  • Mohammed PO, Abdeljawad T, Hamasalh FK. 2021a. Discrete Prabhakar fractional difference and sum operators. Chaos Solit Fractals. 150:111182. doi: 10.1016/j.chaos.2021.111182.
  • Mohammed PO, Abdeljawad T, Hamasalh FK. 2021b. On Riemann—Liouville and Caputo fractional forward difference monotonicity analysis. Mathemat. 9(11):1303. doi: 10.3390/math9111303.
  • Mohammed PO, Almusawa MY. 2023. On analysing discrete sequential operators of fractional order and their monotonicity results. AIMS Math. 8(6):12872–12888. doi: 10.3934/math.2023649.
  • Mohammed PO, Almutairi O, Agarwal RP, Hamed YS. 2022. On convexity, monotonicity and positivity analysis for discrete fractional operators defined using exponential kernels. Fractal Fract. 6(2):55. doi: 10.3390/fractalfract6020055.
  • Mohammed PO, Goodrich CS, Hamasalh FK, Kashuri A, Hamed YS. 2022. On positivity and monotonicity analysis for discrete fractional operators with discrete Mittag–Leffler kernel. Math Methods In App Sci. 45(10):6391–6410. doi: 10.1002/mma.8176.
  • Mozyrska D, Torres DFM, Wyrwas M. 2019. Solutions of systems with the Caputo–Fabrizio fractional delta derivative on time scales. Nonlinear Anal Hybrid Syst. 32:168–176. doi: 10.1016/j.nahs.2018.12.001.
  • Wu G, Baleanu D. 2015. Discrete chaos in fractional delayed logistic maps. Nonlinear Dyn. 80(4):1697–1703. doi: 10.1007/s11071-014-1250-3.