THERMAL SCIENCE

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Yong-Ju Yang

THE EXTENDED VARIATIONAL ITERATION METHOD FOR LOCAL FRACTIONAL DIFFERENTIAL EQUATION

ABSTRACT
An extended variational iteration method within the local fractional derivative is introduced for the first time, where two Lagrange multipliers are adopted. Moreover, the sufficient conditions for convergence of the new variational iteration method are also established.
KEYWORDS
local fractional calculus, variational iteration method, boundary value problems, Lagrange’s multiply
PAPER SUBMITTED: 2020-02-01
PAPER REVISED: 2020-06-20
PAPER ACCEPTED: 2020-06-20
PUBLISHED ONLINE: 2021-01-31
DOI REFERENCE: https://doi.org/10.2298/TSCI200201054Y
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2021, VOLUME 25, ISSUE Issue 2, PAGES [1509 - 1516]
REFERENCES
  1. He, J. H., A Tutorial Review on Fractal Space time and Fractional Calculus, International Journal of Theoretical Physics, 53 (2014), 11, pp. 3698-3718
  2. Wang, Q. L., et al., Fractal Calculus and its Application Explanation of Biomechanism of Polar Bear Hairs, Fractals, 26 (2018), 6, 1850086
  3. Abdon, A., Dumitru, B.,Caputo-Fabrizio Derivative Applied to Groundwater Flow within Confined Aquifer, Journal of Engineering Mechanics, 143 (2017), 5, pp. 1-5
  4. Liu, F. J., et al., Silkworm (Bombyx Mori) Cocoon vs. Wild Cocoon: Multi-Layer Structure and Performance Characterization, Thermal Science, 23 (2019), 4, pp. 2135-2142
  5. Wang, Y., et al., A Fractal Derivative Model for Snow's Thermal Insulation Property, Thermal Science, 23 (2019), 4, pp. 2351-2354
  6. Liu, H. Y., et al., A Fractal Rate Model for Adsorption Kinetics at Solid/Solution Interface, Thermal Science, 23 (2019), 4, pp. 2477-2480
  7. Wang, Q. L., et al., Fractal Calculus and Its Application Explanation of Biomechanism of Polar Hairs (Vol. 26, 1850086, 2018), Fractals, 27 (2019), 5, 1992001
  8. Wang, Q. L., et al., Fractal Calculus and Its Application Explanation of Biomechanism of Polar Hairs (Vol . 26, 1850086, 2018), Fractals, 26 (2018), 6, 1850086
  9. He, J. H., A Fractal Variational Theory for 1-D Compressible Flow in a Microgravity Space, Fractals, 28 (2020), 2, 2050024
  10. He, J. H., A Simple Approach to 1-D Convection-Diffusion Equation and Its Fractional Modification for E Reaction Arising in Rotating Disk Electrodes, Journal of Electroanalytical Chemistry, 854 (2019), 113565
  11. He, J. H., Ain, Q.T., New Promises and Future Challenges of Fractal Calculus: from Two-Scale Thermodynamics to Fractal Variational Principle, Thermal Science, 24 (2020), 2A, pp. 659-681
  12. Ain, Q. T., He, J. H., On Two-Scale Dimension and Its Application, Thermal Science, 23 (2019), 3B, pp. 1707-1712
  13. He, J. H., Ji, F. Y., Two-Scale Mathematics and Fractional Calculus for Thermodynamics, Thermal Science, 23 (2019), 4, pp. 2131-2133
  14. Yang, X. J., Advanced Local Fractional Calculus and Its Applications, World Science Publisher, New York, USA, 2012
  15. Yang, X. J., Baleanu, D., Fractal Heat Conduction Problem Solved by Local Fractional Variation Iteration Method, Thermal Science, 17 (2013), 2, pp. 625-628
  16. He, J. H., A Short Remark on Fractional Variational Iteration Method, Phys. Lett. A, 375 (2011), 38, pp. 3362-3364
  17. Yang, Y. J., et al., A Local Fractional Variational Iteration Method for Laplace Equation within Local Fractional Operators, Abstract and Applied Analysis, 2013 (2013), ID202650
  18. Yang, Y. J., The Fractional Residual Method for Solving the Local Fractional Differential Equations, Thermal Science, 24 (2020), 4, pp. 2535-2542
  19. Yang, Y. J., The Local Fractional Variational Iteration Method a Promising Technology for Fractional Calculus, Thermal Science, 24 (2020), 4, pp. 2605-2614
  20. Yang, Y. J., Wang, S.-Q., An Improved Homotopy Perturbation Method for Solving Local Fractional Non-Linear Oscillators, Journal of Low Frequency Noise Vibration and Active Control, 38 (2019), 3-4, pp. 918-927
  21. He, J. H., Approximate Analytical Solution for Seepage Flow with Fractional Derivatives in Porous Media, Comput. Meth Appl. Mech. Eng., 167 (1998), 1-2, pp. 57-68
  22. Wu, G.-C., Lee, E. W. M., Fractional Variational Iteration Method and its Application, Phys. Lett. A, 374 (2010), 25, pp. 2506-2509
  23. Wu, G. C., Baleanu, D., Variational Iteration Method for the Burgers' flow with Fractional Derivatives - New Lagrange Multipliers, Appl. Math. Model, 37 (2013), 9, pp. 6183-6190
  24. Goswami, P., Solutions of Fractional Differential Equations by Sumudu Transform and Variational Iteration Method, Journal of Non-Linear Science and Applications, 9 (2016), 4, pp.1944-1951
  25. Yang, Y. J., A New Method Solving Local Fractional Differential Equations in Heat Transfer, Thermal Science, 23 (2019), 3A, pp. 1663-1669
  26. Tao, Z. L., et al., Variational Iteration Method with Matrix Lagrange Multiplier for Non-Linear Oscillators, Journal of Low Frequency Noise Vibration and Active Control, 38 (2019), 3-4, pp. 984-991
  27. Ahmad, H., et al., Variational Iteration Algorithm-I with an Auxiliary Parameter for Wave-Like Vibration Equations, Journal of Low Frequency Noise Vibration and Active Control, 38 (2019), 3-4, pp. 1113-1124
  28. He, W., et al., Modified Variational Iteration Method for Analytical Solutions of Non-Linear Oscillators, Journal of Low Frequency Noise Vibration and Active Control, 38 (2019), 3-4, pp. 1178-1183
  29. He, J. H., Latifizadeh, H., A General Numerical Algorithm for Non-Linear Differential Equations by the Variational Iteration Method, International Journal of Numerical Methods for Heat and Fluid-Flow, 30 (2020), 11, pp. 4797-4810
  30. Anjum, N., He, J. H., Laplace Transform: Making the Variational Iteration Method Easier, Applied Mathematics Letters, 92 (2019), June, pp. 134-138
  31. He, J. H., Jin, X., A Short Review on Analytical Methods for the Capillary Oscillator in a Nanoscale Deformable Tube, Mathematical Methods in the Applied Sciences, On-line first, doi.org/10.1002/mma.6321, 2020
  32. He, J. H., The Simpler, the Better: Analytical Methods for Non-Linear Oscillators and Fractional Oscillators, Journal of Low Frequency Noise Vibration and Active Control, 38 (2019), 3-4, pp. 1252-1260
  33. He, J. H., A Short Review on Analytical Methods for to a Fully Fourth Order Non-Linear Integral Boundary Value Problem with Fractal Derivatives, International Journal of Numerical Methods for Heat and Fluid-Flow, 30 (2020), 11, pp. 4937-4943
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The extended variational iteration method for local fractional differential equation

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