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An efficient technique for solving linear and nonlinear wave equations within local fractional operators | ||
| Journal of Hyperstructures | ||
| دوره 6، شماره 2، اسفند 2017، صفحه 136-146 اصل مقاله (258.41 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22098/jhs.2017.2668 | ||
| نویسنده | ||
| Hassan Kamil Jassim* | ||
| Department of Mathematics, Faculty of Education for Pure Sciences, University of Thi-Qar, Nasiriyah, Iraq | ||
| چکیده | ||
| In this paper, we utilize reduced differential transform method (RDTM) to obtain approximate solutions for linear and nonlinear wave equations within local fractional differential operators. The operators are taken in the local fractional sense. The efficiency of the considered method is illustrated by some examples. This method reduces significantly the numerical computations compare with local fractional variational iteration method. The results reveal that the suggested algorithm is very effective and simple and can be applied for other linear and nonlinear problems in sciences and engineering. | ||
| کلیدواژهها | ||
| Local fractional wave equation؛ Local fractional derivative operators؛ Reduced differential transform method | ||
| مراجع | ||
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[1] Y. Cao, W. G. Ma, and L. C. Ma, Local Fractional Functional Method for Solv-ing Diffusion Equations on Cantor Sets, Abstract and Applied Analysis, 2014(2014), 1-6. [2] S. Q. Wang, Y. J. Yang, and H. K. Jassim, Local fractional function decom-position method for solving inhomogeneous wave equations with local fractional derivative, Abstract and Applied Analysis, 2014 (2014), 1-7. [3] S. P. Yan, H. Jafari, and H. K. Jassim, Local Fractional Adomian Decomposition and Function Decomposition Methods for Solving Laplace Equation within Local Fractional Operators, Advances in Mathematical Physics, 2014 (2014), 1-7. [4] Z. P. Fan, H. K. Jassim, R. K. Rainna, and X. J. Yang, Adomian Decompo-sition Method for Three-Dimensional Diffusion Model in Fractal Heat Transfer Involving Local Fractional Derivatives, Thermal Science, 19 (2015) S137-S141. [5] H. Jafari, and H. K. Jassim, Local Fractional Series Expansion Method for Solving Laplace and Schrodinger Equations on Cantor Sets within Local Fractional Oper-ators, International Journal of Mathematics and Computer Research, 2 (2014), 736-744. [6] H. Jafari, and H. K. Jassim, Application of the Local fractional Adomian De-composition and Series Expansion Methods for Solving Telegraph Equation on Cantor Sets Involving Local Fractional Derivative Operators, Journal of Zankoy Sulaimani-Part A, 17 (2015), 15-22. [7] X. J. Yang, Advanced Local Fractional Calculus and Its Applications, World Sci-ence Publisher, New York, NY, USA, (2012). . [8] X.J Yang, Local Fractional Functional Analysis and Its Applications, Asian Aca-demic publisher Limited, Hong Kong (2011). [9] M. S. Hu, R. P. Agarwal, and X. J. Yang, Local fractional Fourier series with application to wave equation in fractal vibrating string, Abstract and Applied Analysis, 2012 (2012) 1-15. [10] X. J. Yang, H. M. Srivastava, and C. Cattani, Local fractional homotopy pertur-bation method for solving fractal partial differential equations arising in mathe-matical physics, Rom.Rep.Phys., 67 (2015), 752-761. [11] H. K. Jassim, The Approximate Solutions of Three-Dimensional Diffusion and Wave Equations within Local Fractional Derivative Operator, Abstract and Ap-plied Analysis, 2016 (2016), 1-5. [12] S. Xu, X. Ling, Y. Zhao and H. K. Jassim, A Novel Schedule for Solving the Two-Dimensional Diffusion in Fractal Heat Transfer, Thermal Science, 19 (2015),99-103. [13] H. Jafari and H. K. Jassim, Local Fractional Variational Iteration Method for Nonlinear Partial Differential Equations within Local Fractional Operators, Ap-plications and Applied Mathematics, 10 (2015), 1055-1065. [14] C. Cattani, H. M. Srivastava, and X.-J. Yang, Fractional Dynamics, Emerging Science Publishers, Berlin and Warsaw, (2015). [15] X. J. Yanga, J. A. Tenreiro Machadob, and H. M. Srivastava, Anew numerical technique for solving the local fractional diffusion equation: Two dimensional ex-tended differential transform approach, Applied Mathematics and Computation, 274 (2016), 143-151. [16] H. Jafari, and H. K. Jassim, Numerical Solutions of Telegraph and Laplace Equa-tions on Cantor Sets Using Local Fractional Laplace Decomposition Method, International Journal of Advances in Applied Mathematics and Mechanics, 2 (2015), 1-8. [17] H. Jafari, and H. K. Jassim, Local Fractional Laplace Variational Iteration Method for Solving Nonlinear Partial Differential Equations on Cantor Sets within Local Fractional Operators, Journal of Zankoy Sulaimani-Part A, 16 (2014), 49-57. [18] H. K. Jassim, C. Unlu, S. P. Moshokoa, C. M. Khalique, Local Fractional Laplace Variational Iteration Method for Solving Diffusion and Wave Equations on Can-tor Sets within Local Fractional Operators, Mathematical Problems in Engineer-ing, 2015 (2015), 1-9. [19] H. Jafari, H. K. Jassim, A new approach for solving a system of local fractional partial differential equations, Applications and Applied Mathematics, 11 (2016) 162-173. [20] H. Jafari, H. K. Jassim, Seithuti P. Moshokoa, and V. M. Ariyan, Reduced differential transform method for partial differential equations within local fractional derivative operators, Advances in Mechanical Engineering, 8 (2016), 1-6. | ||
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