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An Operational Matrix Based on Legendre Polynomials for Solving Fuzzy Fractional-Order Differential Equations

机译：基于勒让德多项式的运算矩阵解模糊分数阶微分方程

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摘要

This paper deals with the numerical solutions of fuzzy fractional differential equations under Caputo-type fuzzy fractionalderivatives of orderα∈0,1. We derived the shifted Legendre operational matrix (LOM) of fuzzy fractional derivatives for the numerical solutions of fuzzy fractional differential equations (FFDEs). Our main purpose is to generalize the Legendre operational matrix to the fuzzy fractional calculus. The main characteristic behind this approach is that it reduces suchproblems to the degree of solving a system of algebraic equations which greatly simplifies the problem. Several illustrative examples areincluded to demonstrate the validity and applicability of the presented technique.
机译：研究了阶数α∈0,1的Caputo型模糊分数阶导数下模糊分数阶微分方程的数值解。对于模糊分数阶微分方程（FFDEs）的数值解，我们导出了模糊分数阶导数的移动Legendre操作矩阵（LOM）。我们的主要目的是将Legendre运算矩阵推广到模糊分数演算。这种方法背后的主要特点是，它可以将此类问题减少到求解代数方程组的程度，从而极大地简化了问题。包括几个说明性示例以证明所提出技术的有效性和适用性。

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