Thermal Science

International Scientific Journal

Find this paper on

Jiang-Jun Liu

SHARMA-TASSO-OLVER EQUATION INVOLVING A NEW TIME FRACTAL DERIVATIVE

ABSTRACT

The Sharma-Tasso-Olver equation with a new time fractal derivative is studied. The fractal Laplace transform, Adomian’s decomposition method and He's polynomials are used to solve the equation. The results demonstrate efficiency and realiability of the proposed method.

KEYWORDS

Sharma-Tasso-Olver equation, Caputo fractal derivative, fractal Laplace transform, Adomian’s decomposition method, He's polynomials

PAPER SUBMITTED: 2020-03-22

PAPER REVISED: 2020-06-26

PAPER ACCEPTED: 2020-06-26

PUBLISHED ONLINE: 2021-03-27

DOI REFERENCE: https://doi.org/10.2298/TSCI200322094L

CITATION EXPORT: view in browser or download as text file

THERMAL SCIENCE YEAR 2021, VOLUME 25, ISSUE No. 3, PAGES [2101 - 2107]

REFERENCES

[1] Barnsley, M. F., Harrington, A. N., The Calculus of Fractal Interpolation Functions, Journal of Approximation Theory, 57 (1989), 1, pp. 14-34

[2] Zähle, M., Harmonic Calculus on Fractals: A Measure Geometric Approach II., Potential Analysis, 357 (2005), 9, pp. 3407-3423

[3] Golmankhaneh, A. K., Baleanu, D., Fractal Calculus Involving Gauge Function, Communications in Non-Linear Science and Numerical Simulation, 37 (2016), 1, pp. 125-130

[4] 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

[5] Parvate, A., Gangal, A. D., Calculus on Fractal Subsets of Real Line Ⅰ: Formulation, Fractals, 17 (2009), 1, pp. 53-81

[6] Parvate, A., Gangal, A. D., Calculus on Fractal Subsets of Real Line Ⅱ: Conjugacy with Ordinary Calculus, Fractals, 19 (2011), 3, pp. 271-290

[7] Golmankhaneh, A. K., Baleanu, D., New Derivatives on the Fractal Subset of Real-Line, Entropy, 18 (2016), 2, Article Number 1

[8] Domany, E., et al., Solutions to the Schrodinger Equation on Some Fractal Lattices, Physical Review B , 28 (1983), 6, pp. 1415-1417

[9] Tarasov, V. E., Fractional Fokker-Planck Equation for Fractal Media, Chaos: An Interdisciplinary Journal of Non-Linear Science, 2 (2005), 15, pp. 461-478

[10] Maitama, S., Zhao, W., Local Fractional Laplace Homotopy Analysis Method for Solving Non-Differentiable Wave Equations on Cantor Sets, Computational and Applied Mathematics, 38 (2019), 2, pp. 1-22

[11] Golmankhaneh, A. K., et al., Lagrangian and Hamiltonian Mechanics on Fractals Subset of Real-Line, International Journal of Theoretical Physics, 52 (2013), 11, pp. 4210-4217

[12] Olver, P. J., Evolution Equations Possessing Infinitely Many Symmetries, J. Math. Phys., 18 (1977), 6, pp. 1212-1215

[13] Salas, A. H., Exact Solutions to a Generalized Sharma-Tasso-Olver Equation, Applied mathematics science, 5 (2011), 46, pp. 2289-2295

[14] Abbasbandy, S., Numerical Solutions of the Integral Equations: Homotopy Perturbation Method and Adomian's Decomposition Method, Applied Mathematics and Computation, 173 (2006), 1, pp. 493-500

[15] Pamuk, S., Solution of the Porous Media Equation by Adomian's Decomposition Method, Physics Letters A, 344 (2005), 2, pp. 184-188

[16] He, J. H., A Short Review on Analytical Methods for to a Fully Fourth-Order Non-linear Integral Boundary Value Problem with Fractal Derivatives, Int. J. Numer. Method H., 30 (2020), 11, pp. 4933-4943

[17] He, J. H., Jin, X., A Short Review on Analytical Methods for the Capillary Oscillator in a Nanoscale Deformable Tube, Math. Method Appl. Sci., On-line first, doi.org/ , 2020, 10.1002/mma.6321

[18] Wen, C., et al., Anomalous Diffusion Modeling by Fractal and Fractional Derivatives, Computers and Mathematics with Applications, 59 (2010), 5, pp. 1754-1758

[19] Wen, C., et al., Soil Infiltration Rates and Hydrology Model Classifications Based on the Hausdorff Fractal Derivative Richards Equation, Applied Mathematics and Mechanics, 39 (2018), 1, pp. 77-82

PDF VERSION [DOWNLOAD]

Sharma-Tasso-Olver equation involving a new time fractal derivative

© 2026 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence