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A NEW ANALYTICAL MODELING FOR FRACTAL BLASIUS EQUATION IN MICROGRAVITY SPACE

CHUNFU WEI

School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo 454003, P. R. China

https://doi.org/10.1142/S0218348X21501905Cited by:3 (Source: Crossref)

Abstract

In this paper, the fractal derivative is employed to define the fractal Blasius equation in a microgravity space arising in fluid dynamics, and its fractal variational principle is successfully established by the fractal semi-inverse transform method. The approximate analytical solution of the fractal Blasius equation is obtained by the variational iteration method. Our results have theoretical significance and practical application value. The example shows the approximate approach is reliable and accurate.

Keywords:

References

1. J. H. He , Approximate analytical solution of Blasius equation, Commun. Nonlinear Sci. Numer. Simul. 3(4) (1998) 260–263. Crossref, Google Scholar
2. A. M. Wazwaz , The variational iteration method for solving two forms of Blasius equation on a half-infinite domain, Appl. Math. Comput. 188 (2007) 485–491. Crossref, Web of Science, Google Scholar
3. S. Kumar, R. Kumar, R. P. Agarwal and B. Samet , A study of fractional Lotka-Volterra population model using Haar wavelet and Adams-Bashforth-Moulton methods, Math. Methods Appl. Sci. (2020), https://doi.org/10.1002/mma.6297. Crossref, Web of Science, Google Scholar
4. J. H. He , Homotopy perturbation technique, Comput. Methods Appl. Mech. Eng. 178 (1999) 257–262. Crossref, Web of Science, Google Scholar
5. J. H. He , Homotopy perturbation method: A new nonlinear analytical technique, Appl. Math. Comput. 135(1) (2003) 73–79. Crossref, Web of Science, Google Scholar
6. S. Kumar , A new analytical modelling for fractional telegraph equation via Laplace transform, Appl. Math. Model. 38 (2014) 3154–3163. Crossref, Web of Science, Google Scholar
7. S. Kumar , A new fractional modeling arising in engineering sciences and its analytical approximate solution, Alex. Eng. J. 52 (2013) 813–819. Crossref, Google Scholar
8. S. Kumar , A new fractional analytical approach for treatment of a system of physical models using Laplace transform, Sci. Iran. B 21(5) (2014) 1693–1699. Web of Science, Google Scholar
9. K. L. Wang , A novel perspective for the fractal Schrödinger equation, Fractals (2020), https://doi.org/10.1142/S0218348X21500936. Google Scholar
10. W. B. Sun , Some local fractional integral inequalities for generalized preinvex functions and applications to numerical quadrature, Fractals 27(5) (2019) 1950071. Link, Web of Science, Google Scholar
11. W. B. Sun and Q. Liu , Hadamard type local fractional integral inequalities for generalized harmonically convex functions and applications, Math. Methods Appl. Sci. 43(9) (2020) 5776–5787. Crossref, Web of Science, Google Scholar
12. S. Kumar, A. Kumar and I. K. Argyros , A new analysis for the Keller-Segel model of fractional order, Numer. Algorithms 75 (2017) 213–228. Crossref, Web of Science, Google Scholar
13. M. Nadeem and S. W. Yao , Solving the fractional heat-like and wave-like equations with variable coefficients utilizing the Laplace homotopy method, Int. J. Numer. Methods Heat Fluid Flow 31(1) (2020) 273–292. Crossref, Web of Science, Google Scholar
14. K. L. Wang , Variational principle for nonlinear oscillator arising in a fractal nano/microelectromechanical system, Math. Methods Appl. Sci. (2020), https://doi.org/10.1002/mma.6726. Crossref, Web of Science, Google Scholar
15. K. L. Wang , A new fractal transform frequency formulation for fractal nonlinear oscillators, Fractals 3(29) (2020) 2150062. Google Scholar
16. C. Ravichandran, N. Valliammal and J. J. Nieto , New results on exact controllability of a class of fractional neutral integro-differential systems with state-dependent delay in Banach spaces, J. Franklin Inst. 356(3) (2019) 1535–1565. Crossref, Web of Science, Google Scholar
17. C. Ravichandran, K. Logeswari and F. Jarad , New results on existence in the framework of Atangana-Baleanu derivative for fractional integro-differential equations, Chaos Solitons Fractals 125 (2019) 194–200. Crossref, Web of Science, Google Scholar
18. K. Jothimani, K. Kaliraj, Z. Hammouch and C. Ravichandran , New results on controllability in the framework of fractional integrodifferential equations with nondense domain, Eur. Phys. J. Plus 134(9) (2019) 441. Crossref, Web of Science, Google Scholar
19. A. S. Shaikh and K. S. Nisar , Transmission dynamics of fractional order typhoid fever model using Caputo-Fabrizio operator, Chaos Solitons Fractals 128 (2019) 355–365. Crossref, Web of Science, Google Scholar
20. B. Ghanbari, S. Kumar and R. Kumar , A study of behaviour for immune and tumor cells in immunogenetic tumour model with non-singular fractional derivative, Chaos Solitons Fractals 133 (2020) 109619. Crossref, Web of Science, Google Scholar
21. H. Ahmad, A. Akgül, T. A. Khan, P. S. Stanimirović and Y. M. Chu , New perspective on the conventional solutions of the nonlinear time-fractional partial differential equations, Complexity 2020 (2020) 8829017. Crossref, Web of Science, Google Scholar
22. K. A. Abro, I. Khan and K. S. Nisar , Novel technique of Atangana and Baleanu for heat dissipation in transmission line of electrical circuit, Chaos Solitons Fractals 129 (2029) 40–45. Crossref, Web of Science, Google Scholar
23. R. Subashini, K. Jothimani, K. S. Nisar and C. Ravichandran , New results on nonlocal functional integro-differential equations via Hilfer fractional derivative, Alex. Eng. J. 59 (2020) 2891–2899. Crossref, Web of Science, Google Scholar
24. A. Shaikh, A. Tassaddiq, K. S. Nisar and D. Baleanu , Analysis of differential equations involving Caputo-Fabrizio fractional operator and its applications to reaction-diffusion equations, Adv. Differ. Equ. 2019 (2019) 178. Crossref, Web of Science, Google Scholar
25. K. L. Wang , He’s frequency formulation for fractal nonlinear oscillator arising in a microgravity space, Numer. Methods Partial Differ. Equ. 37(2) (2020) 1374–1384. Crossref, Web of Science, Google Scholar
26. J. H. He , A tutorial review on fractal spacetime and fractional calculus, Int. J. Theor. Phys. 53 (2014) 3698–3718. Crossref, Web of Science, Google Scholar
27. J. H. He , Fractal calculus and its geometrical explanation, Results Phys. 10 (2018) 272–276. Crossref, Web of Science, Google Scholar
28. K. L. Wang , A study of the fractal foam drainage model in a microgravity space, Math. Methods Appl. Sci. (2021), http://doi.org/10.1002/mma.7428. Crossref, Web of Science, Google Scholar
29. K. L. Wang , A new fractal model for the soliton motion in a microgravity space, Int. J. Numer. Methods Heat Fluid Flow (2020), https://doi.org/10.1108/HFF-05-2020-0247. Crossref, Web of Science, Google Scholar
30. T. J. Miao et al., A fractal analysis of permeability for fractured rocks, Int. J. Heat Mass Transf. 81 (2015) 75–80. Crossref, Web of Science, Google Scholar
31. L. Li and B. M. Yu , Fractal analysis of the effective thermal conductivity of biological media embedded with randomly distributed vascular trees, Int. J. Heat Mass Transf. 67 (2013) 74–80. Crossref, Web of Science, Google Scholar
32. K. J. Wang and K. L. Wang , Variational principles for fractal Whitham-Broer-Kaup equations in shallow water, Fractals 29(3) (2021) 2150028. Link, Web of Science, Google Scholar
33. K. J. Wang , A new fractional nonlinear singular heat conduction model for the human head considering the effect of febrifuge, Eur. Phys. J. Plus 135 (2020) 871. Crossref, Web of Science, Google Scholar
34. K. L. Wang and C. F. Wei , New analytical approach for fractal $K (p, q)$ $K (p, q)$ model, Fractals (2021), https://doi.org/10.1142/S0218348X21501164. Google Scholar
35. K. L. Wang , A novel approach for fractal Burgers-BBM equation and its variational principle, Fractals 29(3) (2021) 2150059. Link, Web of Science, Google Scholar
36. M. Nadeem and F. Q. Li , He-Laplace method for nonlinear vibration systems and nonlinear wave equation, J. Low Freq. Noise Vib. Act. Control 38(3–4) (2019) 1060–1074. Crossref, Web of Science, Google Scholar
37. M. Nadeem and J. H. He , He-Laplace variational iteration method for solving the nonlinear equations arising in chemical kinetics and population dynamics, J. Math. Chem. 59 (2021) 1234–1245. Crossref, Web of Science, Google Scholar
38. M. Nadeem, F. Q. Li and H. Ahmad , Modified Laplace variational iteration method for solving fourth-order parabolic partial differential equation with variable coefficients, Comput. Math. Appl. 78(6) (2019) 2052–2062. Crossref, Web of Science, Google Scholar
39. H. Zhang and M. Nadeem , A novel approach for the analytical solution of nonlinear time-fractional differential equations, Int. J. Numer. Methods Heat Fluid Flow 31(4) (2020) 1069–1084. Crossref, Web of Science, Google Scholar