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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
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