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Numerical comparison of methods for solving linear differential equations of fractional order

Citations

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Cited by:

  1. Xu, Lan, 2009. "The variational iteration method for fourth order boundary value problems," Chaos, Solitons & Fractals, Elsevier, vol. 39(3), pages 1386-1394.
  2. Roman Parovik, 2020. "Mathematical Modeling of Linear Fractional Oscillators," Mathematics, MDPI, vol. 8(11), pages 1-26, October.
  3. He, Ji-Huan, 2009. "Nonlinear science as a fluctuating research frontier," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2533-2537.
  4. Kateryna Marynets, 2021. "Successive Approximation Technique in the Study of a Nonlinear Fractional Boundary Value Problem," Mathematics, MDPI, vol. 9(7), pages 1-19, March.
  5. Deng, Hongmin & Li, Tao & Wang, Qionghua & Li, Hongbin, 2009. "A fractional-order hyperchaotic system and its synchronization," Chaos, Solitons & Fractals, Elsevier, vol. 41(2), pages 962-969.
  6. Yu, Jicheng & Feng, Yuqiang, 2024. "On the generalized time fractional reaction–diffusion equation: Lie symmetries, exact solutions and conservation laws," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).
  7. Tuan Hoang, Manh & Nagy, A.M., 2019. "Uniform asymptotic stability of a Logistic model with feedback control of fractional order and nonstandard finite difference schemes," Chaos, Solitons & Fractals, Elsevier, vol. 123(C), pages 24-34.
  8. Rehman, Mujeeb ur & Idrees, Amna & Saeed, Umer, 2017. "A quadrature method for numerical solutions of fractional differential equations," Applied Mathematics and Computation, Elsevier, vol. 307(C), pages 38-49.
  9. Rashid Nawaz & Laiq Zada & Abraiz Khattak & Muhammad Jibran & Adam Khan, 2019. "Optimum Solutions of Fractional Order Zakharov–Kuznetsov Equations," Complexity, Hindawi, vol. 2019, pages 1-9, December.
  10. Odibat, Zaid M., 2009. "Exact solitary solutions for variants of the KdV equations with fractional time derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 40(3), pages 1264-1270.
  11. Yu, Yongguang & Li, Han-Xiong, 2009. "Application of the multistage homotopy-perturbation method to solve a class of hyperchaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 2330-2337.
  12. Lan, Heng-you & Cui, Yi-Shun, 2009. "A neural network method for solving a system of linear variational inequalities," Chaos, Solitons & Fractals, Elsevier, vol. 41(3), pages 1245-1252.
  13. Odibat, Zaid, 2020. "An optimized decomposition method for nonlinear ordinary and partial differential equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 541(C).
  14. Tomar, Saurabh & Singh, Mehakpreet & Vajravelu, Kuppalapalle & Ramos, Higinio, 2023. "Simplifying the variational iteration method: A new approach to obtain the Lagrange multiplier," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 204(C), pages 640-644.
  15. Soliman, A.A., 2009. "On the solution of two-dimensional coupled Burgers’ equations by variational iteration method," Chaos, Solitons & Fractals, Elsevier, vol. 40(3), pages 1146-1155.
  16. Goh, S.M. & Noorani, M.S.M. & Hashim, I., 2009. "Efficacy of variational iteration method for chaotic Genesio system – Classical and multistage approach," Chaos, Solitons & Fractals, Elsevier, vol. 40(5), pages 2152-2159.
  17. Arikoglu, Aytac & Ozkol, Ibrahim, 2007. "Solution of fractional differential equations by using differential transform method," Chaos, Solitons & Fractals, Elsevier, vol. 34(5), pages 1473-1481.
  18. Md. Habibur Rahman & Muhammad I. Bhatti & Nicholas Dimakis, 2025. "Solutions for Linear Fractional Differential Equations with Multiple Constraints Using Fractional B-Poly Bases," Mathematics, MDPI, vol. 13(19), pages 1-17, September.
  19. Tien, Wei-Chung & Chen, Cha’o-Kuang, 2009. "Adomian decomposition method by Legendre polynomials," Chaos, Solitons & Fractals, Elsevier, vol. 39(5), pages 2093-2101.
  20. Marwan Abukhaled, 2013. "Variational Iteration Method for Nonlinear Singular Two-Point Boundary Value Problems Arising in Human Physiology," Journal of Mathematics, Hindawi, vol. 2013, pages 1-4, February.
  21. Yu, Yongguang & Li, Han-Xiong, 2008. "The synchronization of fractional-order Rössler hyperchaotic systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(5), pages 1393-1403.
  22. Das, S., 2009. "A note on fractional diffusion equations," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 2074-2079.
  23. Gafiychuk, V. & Datsko, B. & Meleshko, V. & Blackmore, D., 2009. "Analysis of the solutions of coupled nonlinear fractional reaction–diffusion equations," Chaos, Solitons & Fractals, Elsevier, vol. 41(3), pages 1095-1104.
  24. Mossa Al-sawalha, M. & Noorani, M.S.M., 2009. "A numeric–analytic method for approximating the chaotic Chen system," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1784-1791.
  25. W. K. Zahra & S. M. Elkholy, 2012. "The Use of Cubic Splines in the Numerical Solution of Fractional Differential Equations," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2012, pages 1-16, August.
  26. Odibat, Zaid M., 2009. "Computational algorithms for computing the fractional derivatives of functions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(7), pages 2013-2020.
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