NEW OPERATIONAL MATRIX OF RIEMANN-LIOUVILLE FRACTIONAL DERIVATIVE OF ORTHONORMAL BERNOULLI POLYNOMIALS FOR THE NUMERICAL SOLUTION OF SOME DISTRIBUTED-ORDER TIME-FRACTIONAL PARTIAL DIFFERENTIAL EQUATIONS

IF 1 4区 数学 Q3 MATHEMATICS, APPLIED
M. Pourbabaee, A. Saadatmandi
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引用次数: 0

Abstract

In this article, the orthonormal Bernoulli polynomials (OBPs) and their properties are applied for concluding a general technique for forming a new operational matrix of the distributed-order (DO) fractional derivative. Then, we apply tau approach and obtained operational matrix to solve some DO time-fractional partial differential equations including distributed-order Rayleigh-Stokes problem (DRSP) for a generalized second-grade fluid and DO anomalous sub-diffusion equation. Our methodology reduces the solution of these problems to a set of algebraic equations. By analysis the error of approximation by the obtained matrix and comparing between the numerical solutions and exact result, we can conclude that this operational matrix is valid to solve the mentioned equations. Also, to confirm the accuracy and the validity of our technique three examples are provided. Finally, we compare obtained results from this approach with the achieved results from relevant studies.
一些分布阶时间分数阶偏微分方程数值解的标准正交伯努利多项式riemann-liouville分数阶导数的新运算矩阵
本文利用正交伯努利多项式及其性质,总结了一种构造分数阶导数新运算矩阵的一般方法。在此基础上,应用tau方法,得到了求解广义二阶流体的分布阶Rayleigh-Stokes问题(DRSP)和DO异常亚扩散方程的运算矩阵。我们的方法将这些问题的解简化为一组代数方程。通过分析所得矩阵的逼近误差,并将数值解与精确结果进行比较,可以得出该运算矩阵对上述方程的求解是有效的。为了验证该方法的准确性和有效性,给出了三个算例。最后,我们将该方法得到的结果与相关研究的结果进行了比较。
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来源期刊
CiteScore
2.30
自引率
9.10%
发文量
45
期刊介绍: The Journal of Applied Analysis and Computation (JAAC) is aimed to publish original research papers and survey articles on the theory, scientific computation and application of nonlinear analysis, differential equations and dynamical systems including interdisciplinary research topics on dynamics of mathematical models arising from major areas of science and engineering. The journal is published quarterly in February, April, June, August, October and December by Shanghai Normal University and Wilmington Scientific Publisher, and issued by Shanghai Normal University.
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