Müntz Sturm-Liouville问题：理论与数值实验
Müntz Sturm-Liouville Problems: Theory and Numerical Experiments
摘要：
本文提出了两类新的Müntz函数，分别称为第一类和第二类Jacobi-Müntz函数。这些新生成的函数满足两个自伴分数阶Sturm-Liouville问题，因而具有正交性、完备性、三项递推关系等谱性质，并由此得到了两个新的正交投影及其误差界.此外，还引入了两个新的Müntz型求积规则。作为基函数的两个应用，考虑了分数阶常微分方程和偏微分方程，并给出了数值结果。
英文摘要：
This paper presents two new classes of Müntz functions which are called Jacobi-Müntz functions of the first and second types. These newly generated functions satisfy in two self-adjoint fractional Sturm-Liouville problems and thus they have some spectral properties such as: orthogonality, completeness, three-term recurrence relations and so on. With respect to these functions two new orthogonal projections and their error bounds are derived. Also, two new Müntz type quadrature rules are introduced. As two applications of these basis functions some fractional ordinary and partial differential equations are considered and numerical results are given.
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