Fractional-order clique functions to solve left-sided Bessel fractional integro-differential equations

IF 5.3 1区 数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Chaos Solitons & Fractals Pub Date : 2025-01-22 DOI:10.1016/j.chaos.2025.116025
P. Rahimkhani , Y. Ordokhani , M. Razzaghi
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Abstract

In this study, we consider a new class of nonlinear integro-differential equations with the Bessel fractional integral-derivative. For solving the considered equations, fractional-order clique functions (FCFs), and some of their properties are introduced. First, we approximate the unknown function and its derivatives/integrals in terms of the FCFs. Then, we substitute these approximations and their derivatives/integrals into the considered equation. The left-sided Bessel fractional derivative/integral (LSBFD/I) of the unknown function is approximated using the properties of the FCFs and LSBFD/I. By collocating the resulting residual function at the well-known shifted Legendre points, we derive a system of nonlinear algebraic equations. In addition, convergence analysis of the proposed approach is discussed. Finally, the presented strategy is applied to some numerical experiments to verify its applicability and accuracy.
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分数阶团函数解左侧贝塞尔分数阶积分微分方程
本文研究了一类具有贝塞尔分数阶积分导数的非线性积分微分方程。为了求解所考虑的方程,引入了分数阶团函数及其一些性质。首先,我们根据fcf近似未知函数及其导数/积分。然后,我们将这些近似及其导数/积分代入所考虑的方程。利用ffc和LSBFD/I的性质对未知函数的左侧贝塞尔分数阶导数/积分(LSBFD/I)进行近似。通过在众所周知的移位的勒让德点处配置得到的残差函数,我们导出了一个非线性代数方程组。此外,还讨论了该方法的收敛性分析。最后,通过数值实验验证了该策略的适用性和准确性。
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来源期刊
Chaos Solitons & Fractals
Chaos Solitons & Fractals 物理-数学跨学科应用
CiteScore
13.20
自引率
10.30%
发文量
1087
审稿时长
9 months
期刊介绍: Chaos, Solitons & Fractals strives to establish itself as a premier journal in the interdisciplinary realm of Nonlinear Science, Non-equilibrium, and Complex Phenomena. It welcomes submissions covering a broad spectrum of topics within this field, including dynamics, non-equilibrium processes in physics, chemistry, and geophysics, complex matter and networks, mathematical models, computational biology, applications to quantum and mesoscopic phenomena, fluctuations and random processes, self-organization, and social phenomena.
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