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

 آمار

تعداد نشریات44
تعداد شماره‌ها1,340
تعداد مقالات16,468
تعداد مشاهده مقاله53,445,103
تعداد دریافت فایل اصل مقاله16,005,110
Akbarpoor, Shahrbanoo, Dabbaghian, Abdol. (1403). Approximate solutions of inverse Nodal problem with conformable derivative. سامانه مدیریت نشریات علمی, 12(3), 610-623. doi: 10.22034/cmde.2023.56851.2380
Shahrbanoo Akbarpoor; Abdol Hadi Dabbaghian. "Approximate solutions of inverse Nodal problem with conformable derivative". سامانه مدیریت نشریات علمی, 12, 3, 1403, 610-623. doi: 10.22034/cmde.2023.56851.2380
Akbarpoor, Shahrbanoo, Dabbaghian, Abdol. (1403). 'Approximate solutions of inverse Nodal problem with conformable derivative', سامانه مدیریت نشریات علمی, 12(3), pp. 610-623. doi: 10.22034/cmde.2023.56851.2380
Akbarpoor, Shahrbanoo, Dabbaghian, Abdol. Approximate solutions of inverse Nodal problem with conformable derivative. سامانه مدیریت نشریات علمی, 1403; 12(3): 610-623. doi: 10.22034/cmde.2023.56851.2380

Approximate solutions of inverse Nodal problem with conformable derivative

Computational Methods for Differential Equations
مقاله 14، دوره 12، شماره 3، مهر 2024، صفحه 610-623    اصل مقاله (428.95 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2023.56851.2380
نویسندگان
Shahrbanoo Akbarpoor1؛ Abdol Hadi Dabbaghian* 2
1Department of Mathematics, Jouybar Branch, Islamic Azad University, Jouybar, Iran.
2Department of Mathematics, Neka Branch, Islamic Azad University, Neka, Iran.
چکیده
Our research is about the Sturm-Liouville equation which contains conformable fractional derivatives of order $\alpha \in (0,1]$ in lieu of the ordinary derivatives. First, we present the eigenvalues, eigenfunctions, and nodal points, and the properties of nodal points are used for the reconstruction of an integral equation. Then, the Bernstein technique was utilized to solve the inverse problem, and the approximation of solving this problem was calculated. Finally, the numerical examples were introduced to explain the results. Moreover,  the analogy of this technique is shown in a numerical example with the Chebyshev interpolation technique .
کلیدواژه‌ها
Inverse problem؛ Conformable fractional؛ Nodal points؛ Bernstein technique؛ Numerical solution
مراجع
  • [1] T. Abdeljawad, On conformable fractional calculus, Journal of Computational and Applied Mathematics., 279 (2015), 57–66.
  • [2] A. Aghazadeh and Y. Mahmoudi, On approximating eigenvalues and eigenfunctions of fractional order SturmLiouville problems, Computational Methods for Differential Equations., 11(4) (2023), 811–821.
  • [3] M. H. T. Alshbool, A. S. Bataineh, I. Hashim, and O. R. Isik, Solution of fractional-order differential equations based on the operational matrices of new fractional Bernstein functions, Journal of King Saud University-Science., 29 (2017), 1–18.
  • [4] A. Atangana, D. Baleanu, and A. Alsaedi, New properties of conformable derivative, Open Math., 13 (2015), 889–898.
  • [5] Y. C¸akmak, Inverse nodal problem for a conformable fractional diffusion operator, Inverse Problems in Science and Engineering., 29(9) (2021), 1308–1322.
  • [6] Y. H. Cheng, The dual eigenvalue problems of the conformable fractional Sturm–Liouville problems, Boundary Value Problems., 83 (2021), 1-10.
  • [7] W. S. Chung, Fractional Newton mechanics with conformable fractional derivative, Journal of Computational and Applied Mathematics., 290 (2015), 150–158.
  • [8] A. A. Dascioglu and N. Isle, Bernstein collocation method for solving nonlinear differential equations, Mathematical and Computational Applications., 18(3) (2013), 293–300.
  • [9] M. Dehghan and A. Mingarelli, Fractional Sturm–Liouville Eigenvalue Problems, II, Fractal Fract., 487(6) (2022).
  • [10] G. Freiling and V. Yurko, Inverse Sturm-Liouville problems and their applications, New York, NOVA Science publishers, 2001.
  • [11] O. H. Hald and J. R. Mclaughlin, Solutions of inverse nodal problems, Inverse Problems., 5 (1989), 307–347.
  • [12] M. Jafari, F. Dastmalchi Saei, A. A. Jodayree Akbarfam, and M. Jahangirirad, The generalized conformable derivative for 4α-order Sturm-Liouville problems , Computational Methods for Differential Equations., 10(3) (2022), 816–825.
  • [13] B. Jin and W. Rundell, An inverse Sturm–Liouville problem with a fractional derivative, Journal of Computational Physics., 231 (2012), 4954–4966.
  • [14] R. Khalil, M. Al Horania, A. Yousefa, and M. Sababheh, A new definition of fractional derivative, Journal of Computational and Applied Mathematics., 264 (2014), 65–70.
  • [15] Y. Khalili and M. Khaleghi Moghadam, The interior inverse boundary value problem for the impulsive SturmLiouville operator with the spectral boundary conditions, Computational Methods for Differential Equations., 10(2) (2022), 519–525.
  • [16] A. Kilbas, H. Srivastava, and J. Trujillo, Theory and applications of fractional differential equations, New York, North-Holland, Math Studies, 2006.
  • [17] H. Koyunbakan, A new inverse problem for the diffusion operator, Applied Mathematics Letters., 19 (2006), 995–999.
  • [18] W. Li, L. Bai, Y. Chen, S. D. Santos, and B. Li, Solution of linear fractional partial differential equations based on the operator matrix of fractional Bernstein polynomials and error correction, International Journal of Innovative Computing and Applications., 14 (2018), 211–226.
  • [19] G. G. Lorentz, Bernstein polynomials, New York, N. Y., Chelsia Publishing Co., 1986.
  • [20] J. R. Mclaughlin, Inverse spectral theory using nodal points as data-a uniqueness result, J.Differential Equations., 73(2) (1988), 354–362.
  • [21] K. S. Miller, An introduction to fractional calculus and fractional differential equations, New York (NY), J Wiley and Sons, 1993.
  • [22] H. Mortazaasl and A. Jodayree Akbarfam, Trace formula and inverse nodal problem for a conformable fractional Sturm-Liouville problem, Inverse Problems in Science and Engineering., 28(4) (2020), 524–555.
  • [23] K. Oldham and J. Spanier, The fractional calculus :theory and applications of differentiation and integration of arbitrary order, New York (NY), Academic Press, 1974.
  • [24] I. Podlubny, Fractional differential equations, San Diago (CA), Academic Press, 1999.
  • [25] M. N. Sahlan and H. Afshari, Three new approaches for solving a class of strongly nonlinear two-point boundary value problems, Bound. Value Probl., 18(1) (2021), 121.
  • [26] A. Sa’idu and H. Koyunbakan, Inverse fractional Sturm-Liouville problem with eigenparameter in the boundary conditions, Math. Meth. Appl. Sci., (2022), 1–10.
  • [27] C. L. Shen, On the nodal sets of the eigenfunctions of the string equations, SIAM Journal on Mathematical Analysis., 19 (1988), 1419–1424.
  • [28] C. T. Shieh and V. A. Yurko, Inverse nodal and inverse spectral problems for discontinuous boundary value problems, J. Math. Anal. Appl., 347 (2008), 266–272.
  • [29] X. Xiaoyong and X. Da, Legendre wavelets method for approximate solution of fractional-order differential equations under multi-point boundary conditions, International Journal of Computer Mathematics., 95(5) (2018), 998–1014.
  • [30] X. F. Yang, Reconstruction of the diffusion operator from nodal data, Verlag der Zeitschrift fur Naturforch., 65(a) (2010), 100–106.
  • [31] E. Yilmaz, H. Koyunbakan, and U. IC, Inverse nodal problem for the differential operator with a singularity at zero, Computer Modeling in Engineering and Sciences., 92 (2013), 303–313.
  • [32] E. Yilmaz and H. Koyunbakan, Reconstruction of potential function and its derivatives for Sturm-Liouville problem with eigenvalues in boundary condition, Inverse Prob. Sci. Eng., 18 (2010), 935–944.
  • [33] H. W. Zhou, S. Yang, and S. Q. Zhang Conformable derivative approach to anomalous diffusion, Physica A: Statistical Mechanics and its Applications., 491 (2018), 1001–1013.
آمار
تعداد مشاهده مقاله: 195
تعداد دریافت فایل اصل مقاله: 370


سامانه مدیریت نشریات علمی. قدرت گرفته از سیناوب