Variational iteration method for n-dimensional time-fractional Navier–Stokes equation

References

• Baleanu D, Diethelm K, Scalas E, et al. Fractional calculus: models and numerical methods. 2nd Ed., Vol. 5. Singapore: World Scientific; 2012.
   Google Scholar
• El-Shorbagy MA, ur Rahman M, Karaca Y. A computational analysis fractional complex-order values by abc operator and Mittag–Leffler kernel modeling. Fractals. 2023;31:Article ID 2340164. doi: 10.1142/S0218348X23401643
   Web of Science ®Google Scholar
• Ur Rahman M, Alhawael G, Karaca Y. Multicompartmental analysis of middle eastern respiratory syndrome coronavirus model under fractional operator with next-generation matrix methods. FRACTALS (fractals). 2023;31(10):1–20.
   Web of Science ®Google Scholar
• Mahmood T, ur Rahman M, Arfan M, et al. Mathematical study of algae as a bio-fertilizer using fractal–fractional dynamic model. Math Comput Simul. 2023;203:207–222. doi: 10.1016/j.matcom.2022.06.028
   Web of Science ®Google Scholar
• Adnan AA, ur Rahmamn M, Shah Z, et al. Investigation of a time-fractional covid-19 mathematical model with singular kernel. Adv Contin Discrete Models. 2022;2022(1):34. doi: 10.1186/s13662-022-03701-z
   PubMedGoogle Scholar
• Alrabaiah H, Ur Rahman M, Mahariq I, et al. Fractional order analysis of hbv and hcv co-infection under abc derivative. Fractals. 2022;30(01):Article ID 2240036.
   Web of Science ®Google Scholar
• Zhang L, ur Rahman M, Haidong Q, et al. Fractal-fractional anthroponotic cutaneous Leishmania model study in sense of Caputo derivative. Alex Eng J. 2022;61(6):4423–4433. doi: 10.1016/j.aej.2021.10.001
   Web of Science ®Google Scholar
• Jaber KK, Ahmad RS. Analytical solution of the time fractional Navier–Stokes equation. Ain Shams Eng J. 2018;9(4):1917–1927. doi: 10.1016/j.asej.2016.08.021
   Web of Science ®Google Scholar
• Jena RM, Chakraverty S. Solving time-fractional Navier–Stokes equations using homotopy perturbation Elzaki transform. SN Appl Sci. 2019;1:1–13.
   Web of Science ®Google Scholar
• Cao S, Weerasekera N, Shingdan DR. Modeling approaches for fluidic mass transport in next generation micro and nano biomedical sensors. Eur J Biol Res. 2022;1(3):1–9.
   Google Scholar
• Albalawi KS, Mishra MN, Goswami P. Analysis of the multi-dimensional Navier–Stokes equation by Caputo fractional operator. Fractal Fract. 2022;6(12):743. doi: 10.3390/fractalfract6120743
   Web of Science ®Google Scholar
• Albalawi KS, Shokhanda R, Goswami P. On the solution of generalized time-fractional telegraphic equation. Appl Math Sci Eng. 2023;31(1):Article ID 2169685. doi: 10.1080/27690911.2023.2169685
   Google Scholar
• Kilicman A, Shokhanda R, Goswami P. On the solution of (n+1)-dimensional fractional m-burgers equation. Alex Eng J. 2021;60(1):1165–1172. doi: 10.1016/j.aej.2020.10.040
   Google Scholar
• Yang X. Numerical approximations of the Navier–Stokes equation coupled with volume-conserved multi-phase-field vesicles system: fully-decoupled, linear, unconditionally energy stable and second-order time-accurate numerical scheme. Comput Methods Appl Mech Eng. 2021;375:Article ID 113600. doi: 10.1016/j.cma.2020.113600
   PubMed Web of Science ®Google Scholar
• Cheng X, Wang L. Invariant analysis, exact solutions and conservation laws of (2+1)-dimensional time fractional Navier–Stokes equations. Proc R Soc A. 2021;477(2250):Article ID 20210220. doi: 10.1098/rspa.2021.0220
   Google Scholar
• Ibraheem GH, Turkyilmazoglu M, Al-Jawary MA. Novel approximate solution for fractional differential equations by the optimal variational iteration method. J Comput Sci. 2022;64:Article ID 101841. doi: 10.1016/j.jocs.2022.101841
   Web of Science ®Google Scholar
• Chu Y-M, Shah NA, Agarwal P, et al. Analysis of fractional multi-dimensional Navier–Stokes equation. Adv Differ Equ. 2021;2021:1–18. doi: 10.1186/s13662-020-03162-2
   Web of Science ®Google Scholar
• Singh BK, Kumar P. Frdtm for numerical simulation of multi-dimensional, time-fractional model of Navier–Stokes equation. Ain Shams Eng J. 2018;9(4):827–834. doi: 10.1016/j.asej.2016.04.009
   Web of Science ®Google Scholar
• Mahmood S, Shah R, Khan H, et al. Laplace Adomian decomposition method for multi dimensional time fractional model of Navier–Stokes equation. Symmetry. 2019;11(2):149. doi: 10.3390/sym11020149
   Google Scholar
• Miller KS, Ross B. An introduction to the fractional calculus and fractional differential equations. Newyork: Willey; 1993.
   Google Scholar
• Kilbas AA, Srivastava HM, Trujillo JJ. Theory and applications of fractional differential equations. Vol. 204. Amsterdam: Elsevier; 2006.
   Google Scholar
• Podlubny I. Fractional differential equations: an introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications. London: Academic Press; 1999. (Mathematics in science and engineering).
   Google Scholar
• Almeida R. A caputo fractional derivative of a function with respect to another function. Commun Nonlinear Sci Numer Simul. 2017;44:460–481. doi: 10.1016/j.cnsns.2016.09.006
   Web of Science ®Google Scholar
• Liang S, Wu R, Chen L. Laplace transform of fractional order differential equations. Electron J Differ Equ. 2015;2015:1–15. doi: 10.1186/s13662-015-0606-4
   Google Scholar
• Mittal E, Pandey RM, Joshi S. On extension of Mittag–Leffler function. Appl Appl Math: Int J (AAM). 2016;11(1):20.
   Google Scholar
• Odibat Z, Momani S. The variational iteration method: an efficient scheme for handling fractional partial differential equations in fluid mechanics. Comput Math Appl. 2009;58(11-12):2199–2208. doi: 10.1016/j.camwa.2009.03.009
   Web of Science ®Google Scholar
• Odibat ZM. A study on the convergence of variational iteration method. Math Comput Model. 2010;51(9-10):1181–1192. doi: 10.1016/j.mcm.2009.12.034
   Google Scholar
• Sakar MG, Ergören H. Alternative variational iteration method for solving the time-fractional Fornberg–Whitham equation. Appl Math Model. 2015;39(14):3972–3979. doi: 10.1016/j.apm.2014.11.048
   Web of Science ®Google Scholar