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A numerical method for solving fractional differential equations

机译：一种求解分数阶微分方程的数值方法

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Purpose The purpose of this paper is to present a computational technique based on Newton-Cotes quadrature rule for solving fractional order differential equation. Design/methodology/approach The numerical method reduces initial value problem into a system of algebraic equations. The method presented here is also applicable to non-linear differential equations. To deal with non-linear equations, a recursive sequence of approximations is developed using quasi-linearization technique. Findings The method is tested on several benchmark problems from the literature. Comparison shows the supremacy of proposed method in terms of robust accuracy and swift convergence. Method can work on several similar types of problems. Originality/value It has been demonstrated that many physical systems are modelled more accurately by fractional differential equations rather than classical differential equations. Therefore, it is vital to propose some efficient numerical method. The computational technique presented in this paper is based on Newton-Cotes quadrature rule and quasi-linearization. The key feature of the method is that it works efficiently for non-linear problems.
机译：目的本文的目的是提出一种基于牛顿-科特斯正交规则的求解分数阶微分方程的计算技术。设计/方法/方法数值方法将初值问题简化为代数方程组。这里介绍的方法也适用于非线性微分方程。为了处理非线性方程，使用准线性化技术开发了近似的递归序列。结果在文献中的几个基准问题上对该方法进行了测试。比较表明，该方法在鲁棒性和快速收敛性方面具有绝对优势。方法可以解决几种类似类型的问题。独创性/价值已经证明，许多物理系统通过分数微分方程而不是经典微分方程可以更准确地建模。因此，提出一种有效的数值方法至关重要。本文提出的计算技术是基于牛顿-科特斯正交规则和准线性化的。该方法的关键特征是它可以有效地解决非线性问题。

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