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Tavan, Saber, Jahangiri Rad, Mohammad, Salimi Shamloo, Ali, Mahmoudi, Yaghoub. (1401). A numerical scheme for solving time-fractional Bessel differential equations. سامانه مدیریت نشریات علمی, 10(4), 1097-1114. doi: 10.22034/cmde.2021.45407.1910
Saber Tavan; Mohammad Jahangiri Rad; Ali Salimi Shamloo; Yaghoub Mahmoudi. "A numerical scheme for solving time-fractional Bessel differential equations". سامانه مدیریت نشریات علمی, 10, 4, 1401, 1097-1114. doi: 10.22034/cmde.2021.45407.1910
Tavan, Saber, Jahangiri Rad, Mohammad, Salimi Shamloo, Ali, Mahmoudi, Yaghoub. (1401). 'A numerical scheme for solving time-fractional Bessel differential equations', سامانه مدیریت نشریات علمی, 10(4), pp. 1097-1114. doi: 10.22034/cmde.2021.45407.1910
Tavan, Saber, Jahangiri Rad, Mohammad, Salimi Shamloo, Ali, Mahmoudi, Yaghoub. A numerical scheme for solving time-fractional Bessel differential equations. سامانه مدیریت نشریات علمی, 1401; 10(4): 1097-1114. doi: 10.22034/cmde.2021.45407.1910

A numerical scheme for solving time-fractional Bessel differential equations

Computational Methods for Differential Equations
مقاله 18، دوره 10، شماره 4، دی 2022، صفحه 1097-1114    اصل مقاله (274.51 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2021.45407.1910
نویسندگان
Saber Tavan1؛ Mohammad Jahangiri Rad* 1؛ Ali Salimi Shamloo2؛ Yaghoub Mahmoudi1
1Department of Mathematics, Tabriz Branch, Islamic Azad University, Tabriz, Iran.
2Department of Mathematics, Shabestar Branch, Islamic Azad University, Shabestar, Iran.
چکیده
The object of this paper devotes on offering an indirect scheme based on time-fractional Bernoulli functions in the sense of Rieman-Liouville fractional derivative which ends up to the high credit of the obtained approximate fractional Bessel solutions. In this paper, the operational matrices of fractional Rieman-Liouville integration for Bernoulli polynomials are introduced. Utilizing these operational matrices along with the properties of Bernoulli polynomials and the least squares method, the fractional Bessel differential equation converts into a nonlinear system of algebraic. To solve these nonlinear algebraic equations which are a prominent the problem, there is a need to employ Newton’s iterative method. In order to elaborate the study, the synergy of the proposed method is investigated and then the accuracy and the efficiency of the method are clearly evaluated by presenting numerical results.
کلیدواژه‌ها
Fractional-order differential equation؛ Caputo and Rieman-Liouville fractional derivative and integral؛ Convergence analysis؛ Bernoulli functions؛ Least square method
مراجع
  • [1]          O. Abdulaziz, I. Hashim, and S. Momani, solving sestem of fractional differential equations by homotopy pertur- bation method, Phys. Let. A, 372(4) (2008), 451-459.
  • [2]          R. S. Adguzel, U. Aksoy, E. Karapinar, and I. M. Erhan, On the solutions of fractional differential equations via Geraghty type hybrid contractions, Appl. Comput. Math, 20(2) (2021), 313-333.
  • [3]          S. A. Alavi, A. Haghighi, A. Yari, and F. Soltanian, A numerical method for solving fractional optimal control problems using the operational matrix of Mott polynomials, Computational Methods for Differential Equations, 10(3) (2022), 755-773, DOI:10.22034/cmde.2021.39419.1728.
  • [4]          A. Arikoglu and I. Ozkol, Solution of fractional integro-differential equations by using fractional differential trans- form method, Chaos Solitons Fractals, 40(2) (2009), 521-529.
  • [5]          E. Ashpazzadeh, M. Lakestani, and A. Fatholahzadeh, Spectral Methods Combined with Operational Matrices for Fractional Optimal Control Problems: A Review, Appl. Comput. Math, 20(2) (2021), 209-235.
  • [6]          A. H. Bhrawy , M. M. Tharwat, and A. Yildirim, A new formula for fractional integrals of Chebyshev polynomials: application for solving multi-term fractional differential equations, Appl. Math. Model, 37(6) (2013), 4245-4252.
  • [7]          A. H. Bhrawy and M. A. Zaky, A shifted fractional-order jacobi orthogonal functions: An application for system  of fractional differential equations, Appl. Math. Model, 40(2) (2016), 832-845.
  • [8]          V. Daftardar-geiji and H. Jafari, Adomian decomposition:a tool for solving a system of fractional differential equations, J.Math. Anal. Appl, 301(2) (2005), 508-518.
  • [9]          E. H. Doha, A. H. Bhrawy, and S. S. Ezz-Eldien, A new Jacobi operational matrix: an application for solving fractional differential equations, Appl. Math. Model, 36(10) (2012), 4931-4943.
  • [10]        A. Gokdogan, E. Unal, and E. Celik, Conformable Fractional Bessel Equation and Bessel Functions, classical Analysis and ODES, (2015), arXiv:1506.07382(math).
  • [11]        N. Haddadi, Y. Ordokhani, and M. Razzaghi, Optimal control of delay systems by using a hybrid functions approximation, J. Optim. Theory. Appl, 153(2) (2012),338-356.
  • [12]        M. S. Hashemi, E. Ashpazzadeh, M. Moharrami, and M. Lakestani, Fractional order Alpert multiwavelets for discretizing delay fractional differential equation of pantograph type, Appl. Numer. Math, 170 (2021), 1-13.
  • [13]        I. Hashim, O. Abdulaziz, and S. Momani,  Homotopy analysis method for fractional IVPs,  Commun. Nonlinear  Sci. Numer. Simul, 14(3) (2009), 674-684.
  • [14]        S. Kazem, S. Abbasbandy, and S. Kumar, Fractional-order legendre functions for solving fractional-order differ- ential equation, Appl Math Model, 37(7) (2013), 5498-5510.
  • [15]        F. Kh. Keshi, B. P. Moghaddam, and A. Aghili, A numerical approach for solving a class of variable-order fractional functional integral equations, Comput. Appl. Math, 37(1) (2018),4821-4834.
  • [16]        A. A. Kilbas, H. M. Srivastava, and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, North-Holland Mathematics studies, 204(2006), 1-523.
  • [17]        B. G. Korenev, Bessel Functions and their Applications, London; New York: Taylor and Francis, 2002.
  • [18]        E. Kreyszig, Introductory Functional Analysis with Applications, John Wiley and Sons Press, New York, 1987.
  • [19]        S. Kumar, D. Kumar, S. Abbasbandy, and M. M. Rashidi, Analytical solution of fractional  Navier-stokes  equation by using modified Laplace decomposition method, Ain Shams Eng. J, 5(2) (2014), 569-574.
  • [20]        Y. Li and N. Sun, Numerical solution of fractional differential equations using the generalized bloc pulse operational matrix, Comput. Math. Apple, 62(3) (2011), 1046-1054.
  • [21]        A. Lotfi, M. Dehghan, and S. A. Yousefi, A nemerical technique for solving fractional optimal control problem, Comput. Math. Appl, 62(3)(2011), 1055-1067.
  • [22]        J. A. T. Machado and B. P. Moghaddam, A Robust Algorithm for Nonlinear Variable-Order Fractional Control Systems with Delay Publication, Int. J. Nonlinear. Sci. Numer. Simul, 19(3-4) (2018), 231-238.
  • [23]        M. Meerschaert and C. Tadjeran, Finite difference approximations for two-sided space -fractional  partial  differ-  ential equations, Appl. Numer. Math, 56(2006), 80-90.
  • [24]        K. S. Miller and B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations, John- Wily and Sons Inc.New York, 1993.
  • [25]        S.  Mockary,  A.  Vahidi,  and  E.  Babolian,  An  efcient  approximate  solution  of  Riesz   fractional   advection-difusion Equation, Computational Methods for Differential Equations,10(2) (2022), 307-319, DOI:10.22034/cmde.2021.41690.1815.
  • [26]        B. P. Moghaddam and J. A. T. Machado, A computational approach for the solution of a class of variable-order fractional integro-differential equations with weakly singular kernels De Gruyter, 20(4) (2017), 1021-1042.
  • [27]        B. P. Moghaddam and J. A. T. Machado, Extended Algorithms for Approximating Variable Order Fractional Derivatives with Applications, Journal of Scientific Computing, 71(3) (2017), 1351-1374.
  • [28]        B. P. Moghaddam, J. A. T. Machado and H. Behforooz, An integro quadratic spline approach for a class of variable-order fractional initial value problems, Chaos, Solitons and Fractals, 102(c) (2017), 354-360.
  • [29]        M. A. Moghaddam, Y. E. Tabriz, and M. Lakestani, Solving fractional optimal control problems using Genocchi polynomials, Computational Methods for Differential Equations, 9(1) (2021), 79-93.
  • [30]        P. Mokhtary, F. GHoreishi, and H. M. Srivastava, The Muntz-Legendre Tau method for fractional differential equations, Appl. Math. Model, 40(2)(2016), 671-684.
  • [31]        S. Momani and K. Al-Khaled, Numerical solutions for systems of fractional differential equations by thr decom- position method, Appl. Math. Comput, 162(3) (2005), 1351-1365.
  • [32]        Z. Odibat and S. Momani, Application of variational iteration method to nonlinear differential equations of  frac-  tional order, Int.J.Nonlinear Sci. Numer.Simul, 7(1) (2006), 27-34.
  • [33]        W. Okrasinski and L. Plociniczak, A not on fractional equation and its asymptotics, fractional calculus and applied analysis, 16(3) (2013), 559-572.
  • [34]        I. Podlubny, Fractional Differential Equations, Academic Prees, San Diego, CA, 1999.
  • [35]        I. Podlubny, Fractional differential equations: An introduction to fractionl derivatives, Fractional Differential equations, to Methods of Their Solution and Some of Their Applications, Elsevier, 1998.
  • [36]        P. Rahimkhani, Y. Ordokhani, and E. Babolian, Fractional-order Bernoulli wavelets and their applications, Appl. Num. Math, 40(17-18) (2016), 8087-8107.
  • [37]        M. Rivero, L. Rodriguez-Germa, and J. J. Trujillo, Linear fractional differential equations with variable coeffi-  cients, A Mathematics Letters, 21(9) (2008), 892-897 .
  • [38]        G. Simmons, Differential Equations: With Applications and Historical Notes, New York: McGraw-Hill Companies, 1972.
  • [39]        S. C. Shiralashetti and A. B. Deshi, An efficient Haar wavelet collocation method for the numerical solution of multi-term fractional differential equations, Nonlinear Dynam, 83(1) (2016), 293-303.
  • [40]        E. Tohidi, A. H. Bhrawy, and Kh. Erfani, A collocation method based on Bernoulli operational matrix for numerical solution of generalized pantograph equation, Appl. Math. Model, 37(6) (2013), 4283-4294.
  • [41]        G. Watson, A Treatise on the Theory of Bessel Functions, 2nd ed., London; New York: Cambridge University Press, 1995.
  • [42]        SH. Yaghoobi, B. P. Moghaddam, and K. Ivaz, An efficient cubic spline approximation for variable-order fractional differential equations with time delay, Nonlinear Dynamics, 87(2) (2017), 815-826.
  • [43]        SH. Yaghoobi, B. P. Moghaddam, and K. Ivaz, A numerical approach for variable-order fractional unified chaotic systems with time-delay, Computational Methods for Differential Equations, 6(4) (2018), 396-410.
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