آمار
| تعداد نشریات | 43 |
| تعداد شمارهها | 1,222 |
| تعداد مقالات | 15,019 |
| تعداد مشاهده مقاله | 50,482,518 |
| تعداد دریافت فایل اصل مقاله | 13,571,027 |
An accurate method for nonlinear local fractional Wave-Like equations with variable coefficients | ||
| Computational Methods for Differential Equations | ||
| مقاله 10، دوره 9، شماره 3، مهر 2021، صفحه 774-787 اصل مقاله (355.38 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22034/cmde.2020.32950.1532 | ||
| نویسندگان | ||
| Djelloul Ziane1؛ Mountassir Hamdi Cherif* 1؛ Kacem Belghaba1؛ Fethi Bin Muhammad Belgacem2 | ||
| 1Laboratory of mathematics and its applications (LAMAP), University of Oran1 Ahmed Ben Bella, Oran, 31000, Algeria. | ||
| 2Department of Mathematics, Faculty of Basic Education, PAAET, Al-Ardhiya, Kuwait. | ||
| چکیده | ||
| The basic motivation of the present study is to apply the local fractional Sumudu variational iteration method (LFSVIM) for solving nonlinear wave-like equations with variable coefficients and within local fractional derivatives. The derivatives operators are taken in the local fractional sense. The results show that the LFSVIM is an appropriate method to find non-differentiable solutions for similar problems. The results of the solved examples showed the flexibility of applying this method and its ability to reach accurate results even with these new differential equations. | ||
| کلیدواژهها | ||
| Sumudu variational iteration method؛ Nonlinear local fractional wave-like equations؛ Local fractional calculus | ||
| مراجع | ||
|
[1] D. Baleanu, J. A. T. Machado, C. Cattani, M. C. Baleanu, and X. J. Yang, Local Fractional Variational Iteration and Decomposition Methods for Wave Equation on Cantor Sets within Local Fractional Operators, Abst. Appl. Anal., A. ID: 535048, 2014 (2014), 6 pp. [2] A. Bouhassoun and M. Hamdi Cherif, Homotopy Perturbation Method For Solving The Fractional Cahn-Hilliard Equation, J. Interdiscip. Math., 18(5) (2015), 513-524. [3] H. Bulut, H. M. Baskonus, and F. B. Belgacem, The Analytical Solutions of Some Fractional Ordinary Differential Equations By Sumudu Transform Method, Abs. Appl. Anal., A. ID: 203875, 2013 (2013), 6pp. [4] C. Chun and S. Abbasbandy, New Application of Variational Iteration Method for Analytic Treatment of Nonlinear Partial Differential Equations, World Appl. Sci. J., 16(12) (2012), 1677-1681. [5] M. Ghoreishi, Adomian Decomposition Method (ADM) for Nonlinear Wave-like Equations with Variable Coefficient, Appl. Math. Sci., 4(49) (2010), 2431-2444. [6] S. Gupta, D. Kumar, and J. Singh, Application of He’s homotopy perturbation method for solving nonlinear wave-like equations with variable coefficients, Int. J. Adv. Appl. Math. Mech., 1(2) (2013), 65-79. [7] M. Hamdi Cherif, K. Belghaba, and D. Ziane, Homotopy Perturbation Method for Solving the Fractional Fisher’s Equation, Int. J. Anal. appl., 10(1) (2016), 9-16. [8] M. Hamdi Cherif and D. Ziane, A new technique for solving systems of nonlinear fractional partial differential equations, Int. J. Anal. appl., 15(2) (2017), 188-197. [9] M. Hamdi Cherif and D. Ziane, Variational iteration method combined with new transform to solve fractional partial differential equations, Univ. J. Math. Appl., 1(2) (2018), 113-120. [10] S. H. M. Hamed, E. A. Yousif, and A. I. Arbab, Analytic and Approximate Solutions of the Space-Time Fractional Schrdinger Equations by Homotopy Perturbation Sumudu Transform Method, Abs. Appl. Anal, A. ID: 863015, 2014 (2014), 13pp. [11] J. H. He, A new approach to nonlinear partial differential equations, Comm. Nonlinear Sci. Numer. Simul., 2 (1997), 230-235. [12] J. H. He, A variational iteration approach to nonlinear problems and its applications, Mech. Appl., 20(1) (1998), 30-31. [13] J. H. He, Variational iteration method for autonomous ordinary differential systems, Appl. Math. Comput., 114(2/3) (2000), 115-123. [14] M. S. Hu, R. P. Agarwal, and X. J. Yang, Local Fractional Fourier Series with Application to Wave Equation in Fractal Vibrating String, Abs. Appl. Anal, A. ID: 567401, 2012 (2012), 15pp. [15] H. K. Jassim, Local fractional variational iteration transform method to solve partial differential equations arising in mathematical physics, Int. J. Adv. Appl. Math. Mech., 3(1) (2015), 71-76. [16] N. A. Khan, O. Abdul Razzaq, and M. Ayyaz, On the solution of fuzzy differential equations by Fuzzy Sumudu Transform, Nonlinear Engineering., 4(1) (2015), 49–60. [17] R. Y. Molliq and M. S. M. Noorani, Solving the Fractional Rosenau-Hyman Equation via Variational Iteration Method and Homotopy Perturbation Method, Int. J. Diff. Equ., 2012, A. ID: 472030 (2012), 14 pp. [18] A. S. V. Ravi Kanth and K. Aruna, He’s variational iteration method for treating nonlinear singular boundary value problems, Comp. Math. Appl., 60 (2010), 821-829. [19] H. M. Srivastava, A.K. Golmankhaneh, D. Baleanu, and X.J. Yang, Local Fractional Sumudu Transform with Application to IVPs on Cantor Sets, Abs. Appl. Anal., A. ID: 176395, 2014 (2014), 7pp. [20] V. Turut and N. G¨uze, On solving Partial Differential Equations of Fractional Order by Using the Variational Iteration Method and Multivariate Pad´e Approximations, Europ. J. Pure. Appl. Math., 6(2) (2013), 147-171. [21] A. Wazwaz, The variational iteration method for rational solutions for KdV, K(2,2), Burgers, and cubic Boussinesq equations, J. Comp. Appl. Math., 207 (2007), 18-23. [22] G. C. Wu, Variational iteration method for solving the time-fractional diffusion equations in porous medium, Chin. Phys B., 21(12) (2012), 1-5. [23] G. C. Wu and E. W. M. Lee, Fractional variational iteration method and its application, Physics Letters A., 374 (2010), 2506-2509. [24] X. J. Yang, Fractional Functional Analysis and Its Applications, Asian Academic, Hong Kong, 2011. [25] X. J. Yang, Local Fractional Calculus and Its Applications, World Science Publisher, New York, USA, 2012. [26] X. J. Yang and D. Baleanu, Fractal Heat Conduction Problem Solved by Local Fractional Variational Iteration Method, Thermal Science., 17(2) (2013), 625-628. [27] X. J. Yang, D. Baleanu, Y. Khan, and S. T. Mohyud-din, Local Fractional Variational Iteration Method for Diffusion and Wave Equation on Cantor Sets, Rom. J. Phys., 59(1-2) (2014), 36-48. [28] Y. J. Yang, D. Baleanu, and X. J. Yang, A Local Fractional Variational Iteration Method for Laplace Equation within Local Fractional Operators, Abs. Appl. Anal., A. ID: 202650, 2013 (2013), 6 pp. [29] Y. J. Yang and L. Q. Hua, Variational Iteration Transform Method for Fractional Differential Equations with Local Fractional Derivative, Abs. Appl. Anal., A. ID: 760957, 2012 (2014), 9pp. [30] A. M. Yang, J. Li, H. M. Srivastava, G. N. Xie, and X. J. Yang, Local Fractional Laplace Variational Iteration Method for Solving Linear Partial Differential Equations with Local Fractional Derivative, Dis. Dyn. Nat. Soc., A. ID:365981, 2014 (2014), 8 pp. [31] D. Ziane, Local Fractional Sumudu Variational Iteration Method for Solving Partial Differential Equations with Local Fractional Derivative, Int. J. Open Prob. Compt. Math., 10(3) (2017), 29-42. [32] D. Ziane, K. Belghaba, and M. Hamdi Cherif, Fractional homotopy perturbation transform method for solving the time-fractional KdV, K(2,2) and Burgers equations, Int. J. Open Prob. Compt. Math., 8(2) (2015), 63-75. [33] D. Ziane, M. Hamdi Cherif, D. Baleanu, K. Belghaba, and M. Al Qurashi, An Efficient Algorithm for Solving Nonlinear Systems of Partial Differential Equations with Local Fractional Operators, Punjab Univ. J. Math., 51(9) (2019), 85-99. [34] D. Ziane, T. Mohyeldin Elzaki, and M. Hamdi Cherif, Elzaki transform combined with variational iteration method for partial differential equations of fractional order, Fund. J. Math. Appl., 1(1) (2018), 102-108. | ||
|
آمار تعداد مشاهده مقاله: 413 تعداد دریافت فایل اصل مقاله: 308 |
||