ArticleNo Access

VARIATIONAL PERSPECTIVE FOR THE FRACTAL THIN FILM EQUATION ARISING IN ELECTROANALYTICAL CHEMISTRY

School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo 454000, P. R. China

https://doi.org/10.1142/S0218348X22500360Cited by:0 (Source: Crossref)

Abstract

The thin film equation is very important in electroanalytical chemistry arising in diffusion–reaction process. Considering the effort of the surface morphology on the diffusion process, the thin film equation is modified by using the fractal derivative, and its fractal variational principle is successfully established according to the semi-inverse method and two-scale transform method. It is very helpful to study the structure of the approximate solution.

Keywords:

References

1. D. B. Patel, K. R. Chauhan and I. Mukhopadhyay, Initializing the commercial viability of ionic liquids for the electrodeposition techniques: A detailed procedure for preparing CdTe thin films with high photo-absorption, J. Electroanal. Chem. 847 (2019) 113233. Crossref, Web of Science, Google Scholar
2. I. K. Muhammad, F. Alzahranni and H. Aatef, Heat transport and nonlinear mixed convective nanomaterial slip flow of Walter-B fluid containing gyrotactic microorganisms, Alex. Eng. J. 59 (2020) 1761–1769. Crossref, Web of Science, Google Scholar
3. C. S. Inagaki et al., Facile synthesis and dopamine sensing application of three component nanocomposite thin films based on polythiophene, gold nanoparticles and carbon nanotubes, J. Electroanal. Chem. 840 (2019) 208–217. Crossref, Web of Science, Google Scholar
4. I. K. Muhammad and F. Alzahranni, Activation energy and binary chemical reaction effect in nonlinear thermal radiative stagnation point flow of Walter-B nanofluid: Numerical computations, Int. J. Mod. Phys. B 13(34) (2020) 2050132. Google Scholar
5. J. H. He, From micro to nano and from science to technology: Nano age makes the impossible possible, Micro Nanosyst. 12(1) (2020) 1–2. Crossref, Google Scholar
6. J. H. He and C. Sun, A variational principle for a thin film equation, J. Math. Chem. 57(9) (2019) 2075–2081. Crossref, Web of Science, Google Scholar
7. J. H. He, A simple approach to one-dimensional convection-diffusion equation and its fractional modification for E reaction arising in rotating disk electrodes, J. Electroanal. Chem. 854 (2019) 113565. Crossref, Web of Science, Google Scholar
8. J. H. He, A tutorial review on fractal spacetime and fractional calculus, Int. J. Theor. Phys. 53(11) (2014) 3698–3718. Crossref, Web of Science, Google Scholar
9. J. H. He, Fractal calculus and its geometrical explanation, Results Phys. 10 (2018) 272–276. Crossref, Web of Science, Google Scholar
10. X. X. Li, D. Tian, C. H. He and J. H. He, A fractal modification of the surface coverage model for an electrochemical arsenic sensor, Electrochim. Acta 296 (2019) 491–493. Crossref, Web of Science, Google Scholar
11. K. L. Wang, A study of fractal foam drainage model in a microgravity space, Math. Methods Appl. Sci. 44(13) (2021) 10530–10540. Crossref, Web of Science, Google Scholar
12. K. L. Wang, He’s frequency formulation for fractal nonlinear oscillator arising in a microgravity space, Numer. Methods Partial Differ. Equ. 37(2) (2021) 1374–1384. Crossref, Web of Science, Google Scholar
13. J. H. He, Some asymptotic methods for strongly nonlinear equations, Int. J. Mod. Phys. B 20 (2006) 1141–1199. Link, Web of Science, Google Scholar
14. 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
15. M. Inc et al., Modified variational iteration method for straight fins with temperature dependent thermal conductivity, Therm. Sci. 22 (2018) S229–S236. Crossref, Web of Science, Google Scholar
16. M. Inc, The approximate and exact solution of the space-and time-fractional Burgers equations with initial conditions by variational iteration method, J. Math. Anal. Appl. 345 (2008) 476–484. Crossref, Web of Science, Google Scholar
17. K. L. Wang, Novel approach for fractal nonlinear oscillators with discontinuities by Fourier series, Fractals 30(1) (2022) 2250009. Link, Web of Science, Google Scholar
18. B. Kilic and M. Inc, Soliton solutions for the Kundu-Eckhaus equation with the aid of unified algebraic and auxiliary equation expansion methods, J. Electromagn. Waves Appl. 30 (2016) 871–879. Crossref, Web of Science, Google Scholar
19. M. Inc, New compacton and solitary pattern solutions of the nonlinear modied dispersive Klein-Gordon equations, Chaos Solitons Fractals 33 (2007) 1275–1284. Crossref, Web of Science, Google Scholar
20. B. Kilic and M. Inc, Optical solitons for the Schrodinger–Hirota equation with power law nonlinearity by the Backlund transformation, Optik 138 (2017) 6467. Crossref, Web of Science, Google Scholar
21. J. G. Liu and Y. F. Zhang, Analytical study of exact solutions of the nonlinear Korteweg–de Vries equation with space–time fractional derivatives, Mod. Phys. Lett. B 32(2) (2018) 1850012. Link, Web of Science, Google Scholar
22. J. G. Liu, X. J. Yang, Y. Y. Feng and P. Cui, On the $(N + 1)$ -dimensional local fractional reduced differential transform method and its applications, Math. Methods Appl. Sci. 43(15) (2020) 8856–8866. Crossref, Web of Science, Google Scholar
23. J. G. Liu, X. J. Yang, Y. Y. Feng, P. Cui and L. L. Geng, On integrability of the higher dimensional time fractional KdV-type equation, J. Geom. Phys. 160 (2021) 104000. Crossref, Web of Science, Google Scholar
24. Q. T. Ain and J. H. He, On two-scale dimension and its applications, Therm. Sci. 23(3B) (2019) 1707–1712. Crossref, Web of Science, Google Scholar
25. J. H. He and F. Y. Ji, Two-scale mathematics and fractional calculus for thermodynamics, Therm. Sci. (2019), https://doi.org/10.2298/TSCI1904131H. Crossref, Web of Science, Google Scholar
26. J. Fan, X. Yang and Y. Liu, Fractal calculus for analysis of wool fiber: Mathematical insight of its biomechanism, J. Eng. Fibers Fabr. (2019), https://doi.org/10.1177/1558925019872200. Web of Science, Google Scholar
27. J. H. He, Variational principles for some nonlinear partial differential equations with variable coefficients, Chaos Solitons Fractals 19(4) (2004) 847–851. Crossref, Web of Science, Google Scholar
28. K. L. Wang and H. Wang, Fractal variational principles for two different types of fractal plasma models with variable coefficients, Fractals (2022), https://doi.org/10.1142/S0218348X22500438. Web of Science, Google Scholar
29. Y. Wu and J. H. He, A remark on Samuelson’s variational principle in economics, Appl. Math. Lett. 84 (2018) 143–147. Crossref, Web of Science, Google Scholar
30. J. H. He, Hamilton’s principle for dynamical elasticity, Appl. Math. Lett. 72 (2017) 65–69. Crossref, Web of Science, Google Scholar
31. Y. Li and C. H. He, A short remark on Kalaawy’s variational principle for plasma, Int. J. Numer. Methods Heat Fluid Flow 27(10) (2017) 2203–2206. Crossref, Web of Science, Google Scholar
32. H. Ahmad and T. A. Khan, Variational iteration algorithm-I with an auxiliary parameter for wave-like vibration equations, J. Low Freq. Noise Vib. 38(3) (2019) 1113–1124. Crossref, Web of Science, Google Scholar
33. 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