دانشگاه مازندران

 آمار

تعداد نشریات31
تعداد شماره‌ها491
تعداد مقالات4,778
تعداد مشاهده مقاله7,410,486
تعداد دریافت فایل اصل مقاله5,529,268
Khalili, Ziba, Bararpour, Ali, Hosseinzadeh, Khashayar, Jafari, Bahram, Domiri Ganji, Davood. (1402). New Approach of Non-Linear Fractional Differential Equations Analytical Solution by Akbari-Ganji’s Method. پژوهشنامه مدیریت اجرایی, 1(1), 12-18. doi: 10.22080/cste.2024.5009
Ziba Khalili; Ali Bararpour; Khashayar Hosseinzadeh; Bahram Jafari; Davood Domiri Ganji. "New Approach of Non-Linear Fractional Differential Equations Analytical Solution by Akbari-Ganji’s Method". پژوهشنامه مدیریت اجرایی, 1, 1, 1402, 12-18. doi: 10.22080/cste.2024.5009
Khalili, Ziba, Bararpour, Ali, Hosseinzadeh, Khashayar, Jafari, Bahram, Domiri Ganji, Davood. (1402). 'New Approach of Non-Linear Fractional Differential Equations Analytical Solution by Akbari-Ganji’s Method', پژوهشنامه مدیریت اجرایی, 1(1), pp. 12-18. doi: 10.22080/cste.2024.5009
Khalili, Ziba, Bararpour, Ali, Hosseinzadeh, Khashayar, Jafari, Bahram, Domiri Ganji, Davood. New Approach of Non-Linear Fractional Differential Equations Analytical Solution by Akbari-Ganji’s Method. پژوهشنامه مدیریت اجرایی, 1402; 1(1): 12-18. doi: 10.22080/cste.2024.5009

New Approach of Non-Linear Fractional Differential Equations Analytical Solution by Akbari-Ganji’s Method

Contributions of Science and Technology for Engineering
دوره 1، شماره 1، خرداد 2024، صفحه 12-18    اصل مقاله (679.82 K)
نوع مقاله: Original Article
شناسه دیجیتال (DOI): 10.22080/cste.2024.5009
نویسندگان
Ziba Khalili1؛ Ali Bararpour1؛ Khashayar Hosseinzadeh* 1؛ Bahram Jafari2؛ Davood Domiri Ganji1
1Department of Mechanical Engineering, Babol Noshirvani University of Technology, Babol, Iran
2Faculty of Engineering Modern Technologies, Amol University of Special Modern Technologies (AUSMT), Amol, Iran
تاریخ دریافت: 15 دی 1402،  تاریخ بازنگری: 14 بهمن 1402،  تاریخ پذیرش: 21 بهمن 1402 
چکیده
The present study examines fractional differential equations (FDEs) as these types ‎of equations are widely used in modeling. FDEs are more difficult to solve than differential equations, which have‎integer order. There are a variety of mathematical methods for solving these ‎equations. An analytical method is utilized in this paper to solve non-linear FDEs.  ‎Akbari-Ganji’s method (AGM) has been used as a new method for solving FDEs. Comparisons ‎are made between the AGM and previously published papers. Several non-linear FDE examples have been solved to illustrate the high performance and quality of the proposed method. Findings show that ‎the AGM is a highly useful and powerful method that can be utilized for FDEs
کلیدواژه‌ها
Fractional Differential Equations؛ Akbari-Ganji’s Method؛ Mathematical Methods
مراجع
  • Sinan, M., Shah, K., Khan, Z. A., Al-Mdallal, Q., & Rihan, F. (2021). On semianalytical study of fractional-order kawahara partial differential equation with the homotopy perturbation method. Journal of Mathematics, 2021. doi:10.1155/2021/6045722.
  • Das, P., Rana, S., & Ramos, H. (2019). Homotopy perturbation method for solving Caputo‐type fractional‐order Volterra‐Fredholm integro‐differential equations. Computational and Mathematical Methods, 1(5). doi:10.1002/cmm4.1047.
  • Javeed, S., Baleanu, D., Waheed, A., Shaukat Khan, M., & Affan, H. (2019). Analysis of Homotopy Perturbation Method for Solving Fractional Order Differential Equations. Mathematics, 7(1), 40. doi:10.3390/math7010040.
  • Gómez-Aguilar, J., Yépez-Martínez, H., Torres-Jiménez, J., Córdova-Fraga, T., Escobar-Jiménez, R., & Olivares-Peregrino, V. (2017). Homotopy perturbation transform method for nonlinear differential equations involving to fractional operator with exponential kernel. Advances in Difference Equations, 2017(1). doi:10.1186/s13662-017-1120-7.
  • Inas, A. A., & Eladdad, E. E. (2022). On Solving Partial Differential Equations by a Coupling of the Homotopy Perturbation Method and a New Integral Transform. Applied Mathematics and Information Sciences, 16(1), 51–57. doi:10.18576/amis/160106.
  • Shabeeb, M. A., Aljaboori, M. A., & Jasim, S. H. (2018). Homotopy Perturbation Method For Solving Coupled Of Partial Differential Equation. مجلة میسان للدراسات الأکادیمیة, 326. doi:10.54633/2333-017-034-029.
  • Ziane, D., & Cherif, M. H. (2018). Variational iteration transform method for fractional differential equations. Journal of Interdisciplinary Mathematics, 21(1), 185–199. doi:10.1080/09720502.2015.1103001.
  • Sontakke, B. R., Shelke, A. S., & Shaikh, A. S. (2019). Solution of Non-Linear Fractional Differential Equations By Variational Iteration Method and Applications. Far East Journal of Mathematical Sciences (FJMS), 110(1), 113–129. doi:10.17654/ms110010113.
  • Singh, B. K., & Kumar, P. (2017). Fractional Variational Iteration Method for Solving Fractional Partial Differential Equations with Proportional Delay. International Journal of Differential Equations, 2017. doi:10.1155/2017/5206380.
  • Sakar, M. G., & Ergören, H. (2015). Alternative variational iteration method for solving the time-fractional Fornberg-Whitham equation. Applied Mathematical Modelling, 39(14), 3972–3979. doi:10.1016/j.apm.2014.11.048.
  • Demir, D. D., & Zeybek, A. (2017). The Numerical Solution of Fractional Bratu-Type Differential Equations. ITM Web of Conferences, 13, 01008. doi:10.1051/itmconf/20171301008.
  • Bansal, M. K., & Jain, R. (2016). Analytical solution of bagley Torvik equation by generalize differential transform. International Journal of Pure and Applied Mathematics, 110(2), 265–273. doi:10.12732/ijpam.v110i2.3.
  • Ünal, E., & Gökdoğan, A. (2017). Solution of conformable fractional ordinary differential equations via differential transform method. Optik, 128, 264–273. doi:10.1016/j.ijleo.2016.10.031.
  • Yang, X. J., Tenreiro Machado, J. A., & Srivastava, H. M. (2016). A new numerical technique for solving the local fractional diffusion equation: Two-dimensional extended differential transform approach. Applied Mathematics and Computation, 274, 143–151. doi:10.1016/j.amc.2015.10.072.
  • Panda, A., Santra, S., & Mohapatra, J. (2022). Adomian decomposition and homotopy perturbation method for the solution of time fractional partial integro-differential equations. Journal of Applied Mathematics and Computing, 68(3), 2065–2082. doi:10.1007/s12190-021-01613-x.
  • Sadeghinia, A., & Kumar, P. (2021). One Solution of Multi-term Fractional Differential Equations by Adomian Decomposition Method: Scientific Explanation. Current Topics on Mathematics and Computer Science Vol. 6, 120–130. doi:10.9734/bpi/ctmcs/v6/11542d.
  • Haq, F., Shah, K., ur Rahman, G., & Shahzad, M. (2018). Numerical solution of fractional order smoking model via laplace Adomian decomposition method. Alexandria Engineering Journal, 57(2), 1061–1069. doi:10.1016/j.aej.2017.02.015.
  • Verma, P., & Kumar, M. (2022). Analytical solution with existence and uniqueness conditions of non-linear initial value multi-order fractional differential equations using Caputo derivative. Engineering with Computers, 38(1), 661–678. doi:10.1007/s00366-020-01061-4.
  • Khalouta, A., & Kadem, A. (2019). A New Method to Solve Fractional Differential Equations: Inverse Fractional Shehu Transform Method. An International Journal (AAM), 14(2), 926–941. http://pvamu.edu/aam
  • Baskonus, H. M., & Bulut, H. (2015). On the numerical solutions of some fractional ordinary differential equations by fractional Adams-Bashforth-Moulton method. Open Mathematics, 13(1), 547–556. doi:10.1515/math-2015-0052.
  • Khalouta, A., & Kadem, A. (2020). An efficient method for solving nonlinear time-fractional wave-like equations with variable coefficients. Tbilisi Mathematical Journal, 12(4). doi:10.32513/tbilisi/1578020573.
  • Jafari, H., Tajadodi, H., & Baleanu, D. (2015). A numerical approach for fractional order riccati differential equation using B-spline operational matrix. Fractional Calculus and Applied Analysis, 18(2), 387–399. doi:10.1515/fca-2015-0025.
  • Keshavarz, E., Ordokhani, Y., & Razzaghi, M. (2016). A numerical solution for fractional optimal control problems via Bernoulli polynomials. JVC/Journal of Vibration and Control, 22(18), 3889–3903. doi:10.1177/1077546314567181.
  • Garrappa, R. (2018). Numerical Solution of Fractional Differential Equations: A Survey and a Software Tutorial. Mathematics, 6(2), 16. doi:10.3390/math6020016.
  • Nagdy, A. S., & Hashem, K. M. (2020). Numerical solutions of nonlinear fractional differential equations by variational iteration method. Journal of Nonlinear Sciences and Applications, 14(02), 54–62. doi:10.22436/jnsa.014.02.01.
  • Meng, Z., Yi, M., Huang, J., & Song, L. (2018). Numerical solutions of nonlinear fractional differential equations by alternative Legendre polynomials. Applied Mathematics and Computation, 336, 454–464. doi:10.1016/j.amc.2018.04.072.
  • Loverro, A. (2004). Fractional calculus: history, definitions and applications for the engineer. Rapport technique, Department of Aerospace and Mechanical Engineering, Univeristy of Notre Dame, Notre Dame, United States.
  • Akbari, M. R., Ganji, D. D., Nimafar, M., & Ahmadi, A. R. (2014). Significant progress in solution of nonlinear equations at displacement of structure and heat transfer extended surface by new AGM approach. Frontiers of Mechanical Engineering, 9(4), 390–401. doi:10.1007/s11465-014-0313-y
آمار
تعداد مشاهده مقاله: 90
تعداد دریافت فایل اصل مقاله: 167


سامانه مدیریت نشریات علمی. قدرت گرفته از سیناوب