THERMAL SCIENCE
International Scientific Journal
THE LOCAL FRACTIONAL VARIATIONAL ITERATION METHOD A PROMISING TECHNOLOGY FOR FRACTIONAL CALCULUS
ABSTRACT
In order to make the local variational iteration algorithm converge faster and more effective, the Sumudu transform is adopted and a proper initial solution is chosen. Some examples are given to show that the presented method is reliable, efficient and easy to implement from a computational viewpoint.
KEYWORDS
PAPER SUBMITTED: 2019-04-25
PAPER REVISED: 2019-10-25
PAPER ACCEPTED: 2019-10-25
PUBLISHED ONLINE: 2020-06-21
THERMAL SCIENCE YEAR
2020, VOLUME
24, ISSUE
Issue 4, PAGES [2605 - 2614]
- Podlubny, I., Fractional Differential Equations, Academic Press, New York, USA, 1999
- Kilbas, A. A., et al., Theory and Applications of Fractional Differential Equations, Elsevier, Amsterdam, The Netherlands, 2006
- Baleanu, D., et al., Fractional calculus models and numerical methods, Series on Complexity, Nonlinearity and Chaos, World Scientific, Boston, Mass., USA, 2012
- Wang, Y., et al., A fractal derivative model for snow's thermal insulation property, Thermal Science, 23 (2019), 4, pp. 2351-2354
- Wang, Y., et al., A Variational Formulation for Anisotropic Wave Traveling in a Porous Medium, Fractals, 27 (2019), 4, 1950047
- Wang, K. L., He, C. H., A Remark on Wang's Fractal Variational Principle, Fractals, 27 (2019), 8, ID 1950134
- He, J. H., A Short Remark on Fractional Variational Iteration Method, Physics Letters A, 375 (2011), 38, pp. 3362-3364
- Ren, Z. F., et al., He's Multiple Scales Method for Nonlinear Vibrations, Journal of Low Frequency Noise, Vibration and Active Control, 38 (2019), 3-4, pp. 1708-1712
- Yu, D. N., et al., Homotopy Perturbation Method With An Auxiliary Parameter For Nonlinear Oscillators, Journal of Low Frequency Noise, Vibration & Active Control, 38 (2019), 3-4, pp. 1540-1554
- Ul Rahman, J., et al., He-Elzaki Method for Spatial Diffusion of Biological Population, Fractals, 27 (2019), 5, 1950069
- Wang, Q. L., et al., Fractal Calculus and Its Application to Explanation of Biomechanism of Polar Bear hairs, Fractals, 26 (2018), 6, 1850086
- He, J. H., et al., A New Fractional Derivative and Its Application to Explanation of Polar Bear Hairs, Journal of King Saud Universe Science, 28 (2016), 2, pp. 190-192
- He, J. H., Li, Z. B. A Fractional Model for Dye Removal, Journal of King Saud Universe Science, 28 (2016), 1, pp. 14-16
- He, J. H., Fractal Calculus and Its Geometrical Explanation, Results in Physics, 10 (2018), Sept., pp. 272-276
- He, J. H., A Simple Approach to One-Dimensional Convection-Diffusion Equation and Its Fractional Modification for E Reaction Arising in Rotating Disk Electrodes, Journal of Electroanalytical Chemistry, 854 (2019), 113565
- Wang, Q. L., et al., Fractal Calculus and its Application to Explanation of Biomechanism of Polar Bear Hairs, Fractals, 26 (2018), 6, ID 1850086
- Yang, Y. J., Wang, S. Q., An Improved Homotopy Perturbation Method for Solving Local Fractional Nonlinear Oscillators, Journal of Low Frequency Noise, Vibration and Active Control, 38 (2019), 3-4, pp. 918-927
- Wang, Y., An, J. Y., Amplitude-frequency Relationship to a Fractional Duffing Oscillator Arising in Microphysics and Tsunami Motion, J. Low Freq. Noise V. A., 38 (2019), 3-4, pp. 1008-1012
- He, J. H., A Tutorial Review on Fractal Spacetime and Fractional Calculus, International Journal of Theoretical Physics, 53 (2014), 11, pp. 3698-3718
- Yang, X. J., Local Fractional Functional Analysis and Its Applications, Asian Academic publisher Limited, Hong Kong, China 2011
- Yang, X. J, Advanced Local Fractional Calculus and Its Applications, World Science publisher, New York, USA, 2012
- Srivastava, H. M., et al., Local Fractional Sumudu Transform with Application to IVPs on Cantor Sets, Abstract and Applied Analysis, 2014 (2014), ID 620529
- He, J. H., Approximate Analytical Solution for Seepage Flow with Fractional Derivatives in Porous Me-dia, Computer Methods in Applied Mechanics and Engineering, 167 (1998), 1-2, pp. 57-68
- He, J. H., A Short Remark on Fractional Variational Iteration Method, Physics Letters A, 375 (2011), 38, pp. 3362-3364
- Yang, X. J., et al., A Local Fractional Variational Iteration Method for Laplace Equation Within Local Fractional Operators, Abstract and Applied Analysis, 2013 (2013), ID 202650
- Anjum, N., He, J. H., Laplace Transform: Making the Variational Iteration Method Easier, Applied Mathematics Letters, 92 (2019), June, pp. 134-138
- He, J. H., et al., Geometrical Explanation of the Fractional Complex Transform and Derivative Chain Rule for Fractional Calculus, Physics Letters A, 376 (2012), 4, pp. 257-259
- He, J. H., Some Asymptotic Methods for Strongly Nonlinear Equations, International Journal of Modern Physics B, 20 (2006), 10, pp. 1141-1199
- He, J. H., Ji, F. Y., Two-Scale Mathematics and Fractional Calculus for Thermodynamics, Thermal Science, 23 (2019), 4, pp. 2131-2133
- Ain, Q. T., He, J. H., On Two-Scale Dimension and Its Applications, Thermal Science, 23 (2019), 3B, pp. 1707-1712
- He, J. H., Ji, F. Y., Taylor Series Solution for Lane-Emden Equation, Journal of Mathematical Chemistry, 57 (2019), 8, pp. 1932-1934
- He, J. H., The Simplest Approach to Nonlinear Oscillators, Results in Physics, 15 (2019), Dec., ID 102546