دانشگاه تبریز
فهرست نشریات دارای اعتبار وزارت علوم، تحقیقات و فناوری
پایگاه استنادی علوم جهان اسلام (ISC)

 آمار

تعداد نشریات45
تعداد شماره‌ها1,453
تعداد مقالات17,785
تعداد مشاهده مقاله58,009,202
تعداد دریافت فایل اصل مقاله19,579,692
Dehestani, Haniye, Ordokhani, Yadollah. (1403). Designing an efficient algorithm for fractional partial integro-differential viscoelastic equations with weakly singular kernel. سامانه مدیریت نشریات علمی, 13(1), 214-232. doi: 10.22034/cmde.2024.57935.2436
Haniye Dehestani; Yadollah Ordokhani. "Designing an efficient algorithm for fractional partial integro-differential viscoelastic equations with weakly singular kernel". سامانه مدیریت نشریات علمی, 13, 1, 1403, 214-232. doi: 10.22034/cmde.2024.57935.2436
Dehestani, Haniye, Ordokhani, Yadollah. (1403). 'Designing an efficient algorithm for fractional partial integro-differential viscoelastic equations with weakly singular kernel', سامانه مدیریت نشریات علمی, 13(1), pp. 214-232. doi: 10.22034/cmde.2024.57935.2436
Dehestani, Haniye, Ordokhani, Yadollah. Designing an efficient algorithm for fractional partial integro-differential viscoelastic equations with weakly singular kernel. سامانه مدیریت نشریات علمی, 1403; 13(1): 214-232. doi: 10.22034/cmde.2024.57935.2436

Designing an efficient algorithm for fractional partial integro-differential viscoelastic equations with weakly singular kernel

Computational Methods for Differential Equations
مقاله 16، دوره 13، شماره 1، فروردین 2025، صفحه 214-232    اصل مقاله (1.71 M)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2024.57935.2436
نویسندگان
Haniye Dehestani؛ Yadollah Ordokhani*
Department of Mathematics, Faculty of Mathematical Sciences, Alzahra University, Tehran, Iran.
چکیده
In this paper, the discretization method is developed by means of Mott-fractional Mott functions (MFM-Fs) for solving fractional partial integro-differential viscoelastic equations with weakly singular kernels. By taking into account the Riemann-Liouville fractional integral operator and operational matrix of integration, we convert the proposed problem to fractional partial integral equations with weakly singular kernels. It is necessary to mention that the operational matrices of integration are obtained with new numerical algorithms. These changes effectively affect the solution process and increase the accuracy of the proposed method. Besides, we investigate the error analysis of the approach. Finally, several examples are solved by applying the discretization method by combining MFM-Fs and the gained results are compared with the methods available in the literature.
کلیدواژه‌ها
Mott-fractional Mott functions؛ Fractional partial integro-differential viscoelastic equations؛ Operational matrices of integration
مراجع
  • [1] K. G. Ali and J. F. Gomez-Aguilar, Approximation of partial integro differential equations with a weakly singular kernel using local meshless method, Alex. Eng. J., 59 (2020), 2091–2100.
  • [2] S. Abbasbandy, S. Kazemb, M. S. Alhuthalic, and H. H. Alsulami, Application of the operational matrix of fractional-order Legendre functions for solving the time-fractional convection-diffusion equation, Appl. Math. Comput., 266 (2015), 31–40.
  • [3] Z. Avazzadeh, M. H. Heydari, and C. Cattani, Legendre wavelets for fractional partial integro-differential viscoelastic equations with weakly singular kernels, Eur. Phys. J. Plus., 134 (2019), 368.
  • [4] M. S. Barikbin, Modified simple equation method (MSEM) for solving nonlinear (3+1) space-time fractional equations, Comput. methods differ. equ., (2023),
  • [5] S. Behera and S. Saha Ray, An operational matrix based scheme for numerical solutions of nonlinear weakly singular partial integro-differential equations, Appl. Math. Comput., 367 (2020), 124771.
  • [6] 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, Comput. methods differ. equ., 11(1), (2023), 81–94.
  • [7] R. M. Christensen, Theory of Viscoelasticity, (Academic Press, New York), 378, 1982.
  • [8] H. Dehestani, Y. Ordokhani, and M. Razzaghi, Fractional-order Legendre–Laguerre functions and their applications in fractional partial differential equations, Appl. Math. Comput., 336 (2018), 433–453.
  • [9] H. Dehestani, Y. Ordokhani, and M. Razzaghi, Fractional-order Bessel functions with various applications, Appl. Math., 64(6) (2019), 637–662.
  • [10] H. Dehestani, Y. Ordokhani, and M. Razzaghi, Application of fractional Gegenbauer functions in variable-order fractional delay-type equations with non-singular kernel derivatives, Chaos Solitons Fractals, 140 (2020), 110111.
  • [11] H. Dehestani, Y. Ordokhani, and M. Razzaghi, An improved numerical technique for distributed-order timefractional diffusion equations, Numer. Methods Partial Differential Eq., 37(3) (2021), 2490–2510.
  • [12] H. Dehestani, Y. Ordokhani, and M. Razzaghi, Pseudo-operational matrix method for the solution of variable-order fractional partial integro-differential equations, Eng. Comput., 37 (2021), 1791–1806.
  • [13] H. Dehestani, Y. Ordokhani, and M. Razzaghi, Fractional-Lucas optimization method for evaluating the approximate solution of the multi-dimensional fractional differential equations, Eng. Comput., 38 (2022), 481–495.
  • [14] M. E. Gurtin and A. C. Pipkin, A general theory of heat conduction with finite wave speeds, Arch. Ration. Mech. Anal., 31 (1968), 113.
  • [15] M. H. Heydari, A new direct method based on the Chebyshev cardinal functions for variable-order fractional optimal control problems, J. Franklin Inst., 355(12) (2018), 4970–4995.
  • [16] A. A. Kilbas, H. M. Srivastava, and J. J. Trujillo, Theory and applications of the fractional differential equations, Mathematical Studies, 204, Elsevier, Amsterdam, 2006.
  • [17] O. K. Kurkcu, A numerical method with a control parameter for integro-differential delay equations with state-dependent bounds via generalized Mott polynomial, Math. Sci., 14 (2020), 43–52.
  • [18] D. Kumar, J. Singh, S. D. Purohit, and R. Swroop, A hybrid analytical algorithm for nonlinear fractional wave-like equations, Math. Model. Nat. Phenom., 14(3) (2019), 304.
  • [19] R. K. Maurya, V. Devi, N. Srivastava, and V. K. Singh, An efficient and stable Lagrangian matrix approach to Abel integral and integro-differential equations, Appl. Math. Comput., 374 (2020), 125005.
  • [20] R. K. Miller, An integro-differential equation for rigid heat conductors with memory, J. Math. Anal. Appl., 66 (1978), 313.
  • [21] F. Mirzaee, S. Alipour, and N. Samadyar, A numerical approach for solving weakly singular partial integrodifferential equations via two-dimensional-orthonormal Bernstein polynomials with the convergence analysis, Numer. Methods Partial Differential Eq., 35(2) (2018), 615–637.
  • [22] J. Mohapatra and S. Natesan, Parameter-uniform numerical methods for singularly perturbed mixed boundary value problems using grid equidistribution, J. Appl. Math. Comput., 37(1) (2011), 247–265.
  • [23] A. Mohebbi, Compact finite difference scheme for the solution of a time fractional partial integro-differential equation with a weakly singular kernel, Math. Meth. Appl. Sci., 40(18) (2017), 7627–7639.
  • [24] A. Panda, J. Mohapatra, and I. Amirali, A second-order post-processing technique for singularly perturbed Volterra integro-differential equations, Mediterr. J. Math., 18 (2021), 231.
  • [25] A. Panda, S. Santra, and J. Mohapatra, Adomian decomposition and homotopy perturbation method for the solution of time fractional partial integro-differential equations, J. Appl. Math. Comput., 68 (2022), 2065–2082.
  • [26] I. Podlubny, Fractional differential equations, Academic Press, NewYork, 1999.
  • [27] E. D. Rainville, Special Functions, The Macmillan Company, New York, 1960.
  • [28] P. Rajput, N. Srivastava, and V. K. Singh, A high order numerical method for the variable order time-fractional reaction-subdiffusion equation, Chi. J. Phys., 85, (2023), 431–444.
  • [29] N. R. Reddy and J. Mohapatra, An efficient numerical method for singularly perturbed two point boundary value problems exhibiting boundary layers, Natl. Acad. Sci. Lett., 38(4) (2015), 355–359.
  • [30] M. Renardy, Mathematical analysis of viscoelastic ows, Annu. Rev. Fluid Mech., 21(1) (1989), 21–34.
  • [31] S. R. Sahu and J. Mohapatra, Numerical investigation of time delay parabolic differential equation involving two small parameters, Eng. Comput., 38(6) (2021), 2882–2899.
  • [32] S. Santra and J. Mohapatra, Numerical analysis of Volterra integro-differential equations with Caputo fractional derivative, Iran J. Sci. Technol. Trans. Sci., 45 (2021), 1815–1824.
  • [33] S. Santra and J. Mohapatra, A novel finite difference technique with error estimate for time fractional partial integro-differential equation of Volterra type, J. Comput. Appl. Math., 400 (2022), 113746.
  • [34] Z. Shafinejhad and M. Zarebnia, Numerical Solution of Fractional Volterra Integro-Differential Equations Using Flatlet Oblique Multiwavelets, Comput. methods differ. equ., (2023).
  • [35] A. Singh, N. Srivastava, S. Singh, and V. K. Singh, Computational technique for multi-dimensional non-linear weakly singular fractional integro-differential equation, Chi. J. Phys., 80 (2022), 305–333.
  • [36] S. Singh, V. K. Patel and V. K. Singh, Convergence rate of collocation method based on wavelet for nonlinear weakly singular partial integro-differential equation arising from viscoelasticity, Numer. Methods Partial Differential Eq., 34(5) (2018), 1781–1798.
  • [37] N. Srivastava, A. Singh, and V. K. Singh, Computational algorithm for financial mathematical model based on European option, Math. Sci., 17 (2023), 467–490.
  • [38] J. Tang and D. Xu, The global behavior of finite difference-spatial spectral collocation methods for a partial integro-differential equation with a weakly singular kernel, Numer. Math. Theor. Meth. Appl. SIAM, 6(3) (2013), 556–570.
  • [39] S. Zaeri, H. Saeedi, and M. Izadi, Fractional integration operator for numerical solution of the integro-partial time fractional diffusion heat equation with weakly singular kernel, Asian Eur. J. Math., 10(4) (2017), 1750071.
آمار
تعداد مشاهده مقاله: 348
تعداد دریافت فایل اصل مقاله: 634


سامانه مدیریت نشریات علمی. قدرت گرفته از سیناوب