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Khasteh, Mohsen, Refahi Sheikhani, Amir Hosein, Shariffar, Farhad. (1403). A numerical approach for solving Caputo-Prabhakar distributed-order time-fractional partial differential equation. سامانه مدیریت نشریات علمی, 12(3), 571-584. doi: 10.22034/cmde.2024.57844.2426
Mohsen Khasteh; Amir Hosein Refahi Sheikhani; Farhad Shariffar. "A numerical approach for solving Caputo-Prabhakar distributed-order time-fractional partial differential equation". سامانه مدیریت نشریات علمی, 12, 3, 1403, 571-584. doi: 10.22034/cmde.2024.57844.2426
Khasteh, Mohsen, Refahi Sheikhani, Amir Hosein, Shariffar, Farhad. (1403). 'A numerical approach for solving Caputo-Prabhakar distributed-order time-fractional partial differential equation', سامانه مدیریت نشریات علمی, 12(3), pp. 571-584. doi: 10.22034/cmde.2024.57844.2426
Khasteh, Mohsen, Refahi Sheikhani, Amir Hosein, Shariffar, Farhad. A numerical approach for solving Caputo-Prabhakar distributed-order time-fractional partial differential equation. سامانه مدیریت نشریات علمی, 1403; 12(3): 571-584. doi: 10.22034/cmde.2024.57844.2426

A numerical approach for solving Caputo-Prabhakar distributed-order time-fractional partial differential equation

Computational Methods for Differential Equations
مقاله 11، دوره 12، شماره 3، مهر 2024، صفحه 571-584    اصل مقاله (1.31 M)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2024.57844.2426
نویسندگان
Mohsen Khasteh1؛ Amir Hosein Refahi Sheikhani* 1؛ Farhad Shariffar2
1Department of Applied Mathematics, Faculty of Mathematical Sciences, Lahijan Branch, Islamic Azad University, Lahijan, Iran.
2Department of Applied Mathematics, Fouman and Shaft Branch, Islamic Azad University, Fouman, Iran.
چکیده
In this paper, we proposed a numerical method based on the shifted fractional order Jacobi and trapezoid methods to solve a type of distributed partial differential equations. The fractional derivatives are considered in the Caputo-Prabhakar type. By shifted fractional-order Jacobi polynomials our proposed method can provide highly accurate approximate solutions by reducing the problem under study to a set of algebraic equations which is technically simpler to handle. In order to demonstrate the error estimates, several lemmas are provided. Finally, numerical results are provided to demonstrate the validity of the theoretical analysis.
کلیدواژه‌ها
Distributed order؛ Caputo-Prabhakar fractional derivative؛ Shifted Jacobi polynomials؛ Trapezoid؛ Numerical method
مراجع
  • [1] H. Aminikhah, A. H. R. Sheikhani, and H. Rezazadeh, Approximate analytical solutions of distributed order fractional Riccati differential equation, Ain Shams Engineering Journal, 9 (2016), 581–588.
  • [2] H. Aminikhah, A. H. R. Sheikhani, T. Houlari, and H. Rezazadeh, Numerical solution of the distributed-order fractional Bagley-Torvik equation, IEEE/CAA Journal of Automatica Sinica, 6 (2017), 760–765.
  • [3] H. Askari and A. Ansari, Fractional calculus of variations with a generalized fractional derivative, Calculus of variations, 7 (2016), 9.
  • [4] A. Ansari, M. H. Derakhshan, and H. Askari, Distributed order fractional diffusion equation with fractional Laplacian in axisymmetric cylindrical configuration, Communications in Nonlinear Science and Numerical Simulation, 113 (2022), 106590.
  • [5] M. A. Abdelkawy, An improved collocation technique for distributed-order fractional partial differential equations, Romanian Reports in Physics, 72 (2020), 104.
  • [6] T. M. Atanackovic, A generalized model for the uniaxial isothermal deformation of a viscoelastic body, Acta Mechanica, 159 (2002), 77–86.
  • [7] A. H. Bhrawy and M. A. Zaky, Numerical simulation of multi-dimensional distributed-order generalized SchrOdinger equations¨ , Nonlinear Dynamics, 89 (2017), 1415–1432.
  • [8] S. Bonyadi, Y. Mahmoudi, M. Lakestani, and M. Jahangiri rad, Numerical solution of space-time fractional PDEs with variable coefficients using shifted Jacobi collocation method, Computational Methods for Differential Equations, 11(1) (2023), 81-94.
  • [9] A. H. Bhrawy and M. A. Zaky, Shifted fractional-order Jacobi orthogonal functions: application to a system of fractional differential equations, Applied Mathematical Modelling, 40 (2016), 832–845.
  • [10] M. Caputo, Mean fractional-order-derivatives differential equations and filters, Annali dell’Universita di Ferrara, 41 (1995), 73–84.
  • [11] M. Dehghan and M. Abbaszadeh, A Legendre spectral element method (SEM) based on the modified bases for solving neutral delay distributed-order fractional damped diffusion-wave equation, Mathematical Methods in the Applied Sciences, 41 (2018), 3476–3494.
  • [12] S. Eshaghi, A. Ansari, R. K. Ghaziani, and M. A. Darani , Fractional Black-Scholes model with regularized Prabhakar derivative, Publications de l’Institut Mathematique, 102(116) (2017), 121–132.
  • [13] N. J. Ford and M. L. Morgado, Distributed order equations as boundary value problems, Computers & Mathematics with Applications, 64 (2012), 2973–2981.
  • [14] M. Fei and C. Huang, Galerkin-Legendre spectral method for the distributed-order time fractional fourth-order partial differential equation, International Journal of Computer Mathematics, 97 (2019) 1–14.
  • [15] R. M. Ganji , H. Jafari, and D. Baleanu, A new approach for solving multi variable orders differential equations with Mittag-Leffler kernel, Chaos, Solitons and Fractals, 130 (2020),109–405.
  • [16] S. Guo, L. Mei, Z. Zhang, and Y. Jiang, Finite difference/spectral-Galerkin method for a two-dimensional distributed-order time-space fractional reaction-diffusion equation, Applied Mathematics Letters, 85 (2018), 157– 163.
  • [17] R. Gorenflo, Y. Luchko, and M. Stojanovi´c, Fundamental solution of a distributed order time-fractional diffusionwave equation as probability density, Fractional Calculus and Applied Analysis, 16 (2013), 297–316.
  • [18] R. Gorenflo, A. A. Kilbas, F. Mainardi, and S.V. Rogosin, Mittag-Leffler functions, related topics and applications (Vol. 2), Berlin: Springer, 2014.
  • [19] R. Garra, R. Gorenflo, F. Polito, and Z. Tomovski,ˇ Hilfer–Prabhakar derivatives and some applications, Applied mathematics and computation, 242 (2014), 576-589.
  • [20] T. T. Hartley and C. F. Lorenzo, Fractional-order system identification based on continuous order-distributions Signal processing, 83 (2003), 2287–2300.
  • [21] M. H. Heydari, M. Razzaghi, and D. Baleanu, A numerical method based on the piecewise Jacobi functions for distributed-order fractional SchrOdinger equation¨ , Communications in Nonlinear Science and Numerical Simulation, 116 (2023), 106873.
  • [22] E. Kharazmi and M. Zayernouri, Fractional pseudo-spectral methods for distributed-order fractional PDEs, International Journal of Computer Mathematics, 95 (2018), 1340–1361.
  • [23] A.A. Kilbas, M. Saigo, and R. K. Saxena, Generalized Mittag-Leffler function and generalized fractional calculus operators, Integral Transforms and Special Functions, 15(1) (2004), 31–49.
  • [24] Y. Kumar, N. Srivastava, A. Singh, and V. K. Singh, Wavelets based computational algorithms for multidimensional distributed order fractional differential equations with nonlinear source term, Computers & Mathematics with Applications, 132 (2023), 73–103.
  • [25] X.Y. Li and B.Y. Wu, A numerical method for solving distributed order diffusion equations, Applied Mathematics Letters, 53 (2016), 92–99.
  • [26] Y. Luchko, Boundary value problems for the generalized time-fractional diffusion equation of distributed order, Fractional Calculus and Applied Analysis, 12 (2009), 409–422.
  • [27] F. S. Md Nasrudin, and C. Phang, Numerical solution via operational matrix for solving Prabhakar fractional differential equations, Journal of Mathematics, 2022.
  • [28] Z. Mahboob Dana, H. S. Najafi, and A. H. Refahi Sheikhani, An efficient numerical method for solving BenjaminBona-Mahony–Burgers equation using difference scheme, Journal of Difference Equations and Applications, 26 (2020), 1–12.
  • [29] M. Mashoof and A. H. Refahi Sheikhani, Simulating the solution of the distributed order fractional differential equations by block-pulse wavelets, UPB Sci. Bull., Ser. A: Appl. Math. Phys, 79 (2017), 193–206.
  • [30] M. Mashoof, A. H. Refahi Sheikhani, and H.S. Najafi, Stability analysis of distributed-order Hilfer–Prabhakar systems based on Inertia theory, Mathematical Notes, 104 (2018), 74–85.
  • [31] M. Mashoof, A. H. Refahi Sheikhani, and H. S. NAJA, Stability analysis of distributed order Hilfer-Prabhakar differential equations, Hacettepe Journal of Mathematics and Statistics, 47 (2018), 299–315.
  • [32] M. L. Morgado, M. Rebelo, L. L. Ferras, and N. J. Ford, Numerical solution for diffusion equations with distributed order in time using a Chebyshev collocation method, Applied Numerical Mathematics, 114 (2017), 108–123.
  • [33] S. Mashayekhi and M. Razzaghi, Numerical solution of distributed order fractional differential equations by hybrid functions, Journal of Computational Physics, 315 (2016), 169–181.
  • [34] M. L. Morgado and M. Rebelo, Numerical approximation of distributed order reaction-diffusion equations, Journal of Computational and Applied Mathematics, 275 (2015), 216–227.
  • [35] S. Mockary, A. Vahidi, and E. Babolian, An efficient approximate solution of Riesz fractional advection-diffusion equation, Computational Methods for Differential Equations, 10(2) (2022), 307–319.
  • [36] Y. Niu, Y. Liu, H. Li, and F. Liu, Fast high-order compact difference scheme for the nonlinear distributed-order fractional Sobolev model appearing in porous media, Mathematics and Computers in Simulation, 203 (2023), 387–407.
  • [37] P. Pirmohabbati, A. H. R. Sheikhani, H. S. Najafi, and A. A. Ziabari, Numerical solution of full fractional Duffing equations with Cubic-Quintic-Heptic nonlinearities, AIMS Mathematics, 5 (2020), 1621–1641.
  • [38] M. Pourbabaee and A. Saadatmandi, A new operational matrix based on Mu¨ntz–Legendre polynomials for solving distributed order fractional differential equations, Mathematics and Computers in Simulation, 194 (2022), 210–235.
  • [39] P. Rahimkhani, Y. Ordokhani, and E. Babolian,Fractional-order Bernoulli wavelets and their applications, Applied Mathematical Modelling, 40 (2016), 8087–8107.
  • [40] P. Rahimkhani and Y. Ordokhani, Solving of partial differential equations with distributed order in time using fractional-order Bernoulli-Legendre functions, Computational Methods for Differential Equations, 9(3) (2021), 799–817.
  • [41] D. Singh, F. Sultana, and R. K. Pandey, Approximation of Caputo-Prabhakar derivative with application in solving time fractional advection-diffusion equation, International Journal for Numerical Methods in Fluids, 94(7) (2022), 896–919.
  • [42] J. Singh, A. Gupta, and D. Kumar, Computational Analysis of the Fractional Riccati Differential Equation with Prabhakar-type Memory, Mathematics, 11(3) (2023), 644.
  • [43] S. Sabermahani and Y. Ordokhani, An optimum solution for multi-dimensional distributed-order fractional differential equations, Computational Methods for Differential Equations, 11(3) (2023), 548-563.
  • [44] Y. Xu, Y. Zhang, and J. Zhao, Error analysis of the Legendre-Gauss collocation methods for the nonlinear distributed-order fractional differential equation, Applied Numerical Mathematics, 142 (2019), 122–138.
  • [45] B. Yuttanan and M. Razzaghi, Legendre wavelets approach for numerical solutions of distributed order fractional differential equations, Applied Mathematical Modelling, 70 (2019), 350–364.
  • [46] H. Ye, F. Liu, and V. Anh, Compact difference scheme for distributed-order time-fractional diffusion-wave equation on bounded domains, Journal of Computational Physics, 298 (2015), 652–660.
  • [47] F. Zhou, Y. Zhao, Y. Li, and Y.Q. Chen, Design, implementation and application of distributed order PI control, ISA transactions, 52 (2013), 429–437.
  • [48] M. A. Zaky, E.H. Doha, and J. A. Tenreiro Machado, A spectral numerical method for solving distributed-order fractional initial value problems, Journal of Computational and Nonlinear Dynamics, 13 (2018), 101007–101012.
  • [49] H. Zhang, F. Liu, X. Jiang, F. Zeng, and I. Turner, A Crank-Nicolson ADI Galerkin–Legendre spectral method for the two-dimensional Riesz space distributed-order advection-diffusion equation, Computers and Mathematics with Applications, 76 (2018), 2460–2476.
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