تعداد نشریات | 31 |
تعداد شمارهها | 743 |
تعداد مقالات | 7,073 |
تعداد مشاهده مقاله | 10,149,448 |
تعداد دریافت فایل اصل مقاله | 6,857,424 |
Triangular functions method for numerical solution of fractional Mathieu equation | ||
Computational Sciences and Engineering | ||
مقاله 2، دوره 2، شماره 1، تیر 2022، صفحه 1-8 اصل مقاله (292.86 K) | ||
نوع مقاله: Original Article | ||
شناسه دیجیتال (DOI): 10.22124/cse.2022.21911.1025 | ||
نویسندگان | ||
Leila Mansouri1؛ Esmail Babolian2؛ Zahra Azimzadeh* 1 | ||
1Department of Mathematics, College of Science, Yadegar-e-Emam Khomeyni (RAH) Shahr-e-Rey Branch, Islamic Azad University, Tehran, Iran | ||
2Faculty of Mathematical Sciences and Computer, Kharazmi University, 50 Taleghani Avenue, Tehran, 1561836314, Iran | ||
چکیده | ||
Fractional differential equations (FDEs) have recently attracted much attention. Fractional Mathieu equation is a well-known FDE. Here, a method based on operational matrix of triangular functions for fractional order integration is introduced for the numerical solution of fractional Mathieu equation.This technique is a successful method because of reducing the problem to a system of linear equations. By solving this system, an approximate solution is obtained. Illustrative examples demonstrate accuracy and efficiency of the method. | ||
کلیدواژهها | ||
Fractional Mathieu equation؛ Caputo derivative؛ Triangular functions؛ Operational matrix | ||
مراجع | ||
[1] Richard, L. M. (2004). Fractional calculus in bioengineering. Critical Reviews in Biomedical Engineering, 32. [2] Benson, D. A., Meerschaert, M. M., & Revielle, J. (2013). Fractional calculus in hydrologic modeling: A numerical perspective. Advances in water resources, 51, 479-497. [3] Arqub, O. A., El-Ajou, A., & Momani, S. (2015). Constructing and predicting solitary pattern solutions for nonlinear time-fractional dispersive partial differential equations. Journal of Computational Physics, 293, 385-399. [4] Hajikarimi, P., & Moghadas Nejad F. (2021). Mechanical models of viscoelasticity, Applications of Viscoelasticity, Elsevier, 27-62. [5] Kumar, D., Singh, J., & Baleanu, D. (2018). A new analysis of the Fornberg-Whitham equation pertaining to a fractional derivative with Mittag-Leffler-type kernel. The European Physical Journal Plus, 133(2), 1-10. [6] Sabermahani, S., Ordokhani, Y., & Yousefi, S. A. (2018). Numerical approach based on fractional-order Lagrange polynomials for solving a class of fractional differential equations. Computational and Applied Mathematics, 37(3), 3846-3868. [7] Razzaghi, M. (2016). The numerical solution of the Bagley–Torvik equation with fractional Taylor method. Journal of Computational and Nonlinear Dynamics, 11, 051010-1. [8] Vargas, A. M. (2022). Finite difference method for solving fractional differential equations at irregular meshes. Mathematics and Computers in Simulation, 193, 204-216. [9] Tural-Polat, S. N., & Dincel, A. T. (2022). Numerical solution method for multi-term variable order fractional differential equations by shifted Chebyshev polynomials of the third kind. Alexandria Engineering Journal, 61(7), 5145-5153. [10] Pirmohabbati, P., Sheikhani, A. R., Najafi, H. S., & Ziabari, A. A. (2019). Numerical solution of fractional mathieu equations by using block-pulse wavelets. Journal of Ocean Engineering and Science, 4(4), 299-307. [11] Rand, R. H. (2012). Lecture notes on nonlinear vibrations. [12] Najafi, H. S., Mirshafaei, S. R., & Toroqi, E. A. (2012). An approximate solution of the Mathieu fractional equation by using the generalized differential transform method (GDTM). Applications and Applied Mathematics: An International Journal (AAM), 7(1), 24. [13] Deb, A., Dasgupta, A., & Sarkar, G. (2006). A new set of orthogonal functions and its application to the analysis of dynamic systems. Journal of the Franklin Institute, 343(1), 1-26. [14] Babolian, E., Mokhtari, R., & Salmani, M. (2007). Using direct method for solving variational problems via triangular orthogonal functions. Applied mathematics and computation, 191(1), 206-217. [15] Babolian, E., Masouri, Z., & HATAMZADEH, V. S. (2009). A direct method for numerically solving integral equations system using orthogonal triangular functions. [16] Babolian, E., Masouri, Z., & Hatamzadeh-Varmazyar, S. (2009). Numerical solution of nonlinear Volterra–Fredholm integro-differential equations via direct method using triangular functions. Computers & Mathematics with applications, 58(2), 239-247. [17] Han, Z. Y., Li, S. R., & Cao, Q. L. (2012). Triangular orthogonal functions for nonlinear constrained optimal control problems. Research Journal of Applied Sciences, Engineering and Technology, 4(12), 1822-1827. [18] Babolian, E., Maleknejad, K., Roodaki, M., & Almasieh, H. (2010). Two-dimensional triangular functions and their applications to nonlinear 2D Volterra-Fredholm integral equations. Computers & Mathematics with Applications, 60(6), 1711-1722. [19] Kenneth S.. Miller, & Ross, B. (1993). An introduction to the fractional calculus and fractional differential equations. Wiley. [20] Caputo, M. (1967). Linear models of dissipation whose Q is almost frequency independent—II. Geophysical Journal International, 13(5), 529-539. [21] Hatamzadeh-Varmazyar, S., & Masouri, Z. (2019). Numerical solution of second kind Volterra and Fredholm integral equations based on a direct method via triangular functions. International Journal of Industrial Mathematics, 11(2), 79-87. | ||
آمار تعداد مشاهده مقاله: 535 تعداد دریافت فایل اصل مقاله: 451 |