In this paper, we discuss the numerical approximation to solve regular tempered fractional Sturm‐Liouville problem (TFSLP) using finite difference method. The tempered fractional differential operators considered here are of Caputo type. The numerically obtained eigenvalues are real, and the corresponding eigenfunctions are orthogonal. The obtained eigenfunctions work as basis functions of weighted Lebesgue integrable function space $L_w^2$ (a,b). Further, the obtained eigenvalues and corresponding eigenfunctions are used to provide weak solution of the tempered fractional diffusion equation. Approximation and error bounds of the solution of the tempered fractional diffusion equation are provided.

中文翻译：

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回火分数Sturm-Liouville问题的数值逼近及其在分数扩散方程中的应用

在本文中，我们讨论了使用有限差分法求解正则化分数分数Sturm-Liouville问题（TFSLP）的数值逼近。这里考虑的回火分数微分算子是Caputo类型的。数值获得的特征值是实数，相应的特征函数是正交的。获得的本征函数作为加权Lebesgue可积函数空间的基函数${\mathrm{大号}}_w^2$（a，b）。此外，所获得的特征值和相应的特征函数用于提供回火分数扩散方程的弱解。给出了回火分数扩散方程解的近似和误差界。