پیوندهای مفید
آمار
| تعداد نشریات | 20 |
| تعداد شماره‌ها | 547 |
| تعداد مقالات | 8,302 |
| تعداد مشاهده مقاله | 18,870,371 |
| تعداد دریافت فایل اصل مقاله | 6,361,168 |
A new technique of reduce differential transform method to solve local fractional PDEs in mathematical physics | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 4، دوره 12، شماره 1، مرداد 2021، صفحه 37-44 اصل مقاله (141.33 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2021.4653 | ||
| نویسندگان | ||
| Hassan Kamil Jassim* 1؛ Javad Vahidi2 | ||
| 1Department of Mathematics, Faculty of Education for Pure Sciences, University of Thi-Qar, Nasiriyah, Iraq. | ||
| 2Department of Mathematics, Iran University of Science and Technology, Tehran 1684613114, Iran. Department of Mathematical Sciences, University of South Africa, Pretoria 0002, South Africa. | ||
| تاریخ دریافت: 29 مهر 1399، تاریخ پذیرش: 13 آذر 1399 | ||
| چکیده | ||
| In this manuscript, we investigate solutions of the partial differential equations (PDEs) arising in mathematical physics with local fractional derivative operators (LFDOs). To get approximate solutions of these equations, we utilize the reduce differential transform method (RDTM) which is based upon the LFDOs. Illustrative examples are given to show the accuracy and reliable results. The obtained solutions show that the present method is an efficient and simple tool for solving the linear and nonlinear PDEs within the LFDOs. | ||
| کلیدواژه‌ها | ||
| Local fractional RDTM؛ Diffusion equation, Klein-Gordon equation, Schrodinger equation, Nonlinear gas dynamic equation, Local fractional derivative operators | ||
| مراجع | ||
|
[1] S. Q. Wang, Y. J. Yang and H. K. Jassim, Local fractional function decomposition method for solving inhomogeneous wave equations with local fractional derivative, Abstract and Applied Analysis 2014 (2014), ID 176395, 1–7. [2] Y. Cao, W.G. Ma, and L.C. Ma, Local fractional functional method for solving diffusion equations on Cantor sets, Abstract and Applied Analysis 2014 (2014), ID 803693, 1–6. [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), ID 161580, 1–7. [4] Z.P. Fan, H.K. Jassim, R.K. Raina, and X.J. Yang, Adomian Decomposition Method for Three-Dimensional Diffusion Model in Fractal Heat Transfer Involving Local Fractional Derivatives, Thermal Science 19 (2015) 137–141. [5] Y. Zhao, D.F. Cheng, and X.J. Yang, Approximation Solutions for Local Fractional Schrödinger Equation in the One-Dimensional Cantorian System, Advances in Mathematical Physics 2013 (2013), ID 291386, 1–5. [6] A.M. Yang, Y.Z. Zhang, C. Cattani, Application of Local Fractional Series Expansion Method to Solve Klein-Gordon Equations on Cantor Sets, Abstract and Applied Analysis 2014 (2014), ID 372741, 1–6. [7] X.J. Yang, Advanced Local Fractional Calculus and Its Applications, World Science Publisher, New York, NY, USA, 2012. [8] X.J. Yang, Local Fractional Functional Analysis and Its Applications, Asian Academic, Hong Kong, China, 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), Article ID 567401, 1–15. [10] Y.J. Yang, D. Baleanu, and X.J. Yang, Analysis of fractal wave equations by local fractional Fourier series method, Advances in Mathematical Physics 2013 (2013), Article ID 632309, 1–6. [11] X. J. Yang, J. T. Machado, J. Hristov, Nonlinear dynamics for local fractional Burger equation arising in fractal flow, Nonlinear Dyn. 80 (2015) 1661–1664. [12] S. Xu, X. Ling, Y. Zhao, H.K. Jassim, A Novel Schedule for Solving the Two-Dimensional Diffusion in Fractal Heat Transfer, Thermal Science 19 (2015) 99–103. [13] H. K. Jassim, et al., Fractional variational iteration method to solve one dimensional second order hyperbolic telegraph equations, Journal of Physics: Conference Series 1032 (1) (2018) 1–9. [14] H. Jafari, H.K. Jassim, F. Tchier, D. Baleanu, On the Approximate Solutions of Local Fractional Differential Equations with Local Fractional Operator, Entropy 18 (2016) 1–12. [15] X.J. Yanga, J.A. Tenreiro Machadob, H.M. Srivastava, A new numerical technique for solving the local fractional diffusion equation: Two dimensional extended differential transform approach, Applied Mathematics and Computation 274 (2016) 143–151. [16] H.K. Jassim, Analytical Approximate Solutions for Local Fractional Wave Equations, Mathematical Methods in the Applied Sciences 43(2) (2020) 939–947. [17] X. J. Yang, H. M. Srivastava, and C. Cattani, Local fractional homotopy perturbation method for solving fractal partial differential equations arising in mathematical physics, Rom. Rep. Phys. 67 (2015) 752–761. [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 Cantor Sets within Local Fractional Operators, Mathematical Problems in Engineering 2015 (2015), ID 309870, 1–9. [19] H. Jafari, H.K. Jassim, S.P. Moshokoa, V.M. Ariyan, and F. Tchier, Reduced differential transform method for partial differential equations within local fractional derivative operators, Advances in Mechanical Engineering 8 (2016) 1-6. [20] H. Jafari, H. K. Jassim, and J. Vahidi, Reduced Differential Transform and Variational Iteration Methods for 3D Diffusion Model in Fractal Heat Transfer within Local Fractional Operators, Thermal Science 22 (2018) S301–S307. | ||
|
آمار تعداد مشاهده مقاله: 3,094 تعداد دریافت فایل اصل مقاله: 913 |
||