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Müntz sturm-liouville problems: Theory and numerical experiments
Fractional Calculus and Applied Analysis ( IF 3 ) Pub Date : 2021-06-01 , DOI: 10.1515/fca-2021-0034
Hassan Khosravian-Arab 1 , Mohammad Reza Eslahchi 2
Affiliation  

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.

中文翻译:

Müntz Sturm-liouville 问题:理论和数值实验

本文介绍了两类新的 Müntz 函数,它们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随分数 Sturm-Liouville 问题,因此它们具有一些谱性质,例如:正交性、完备性、三项递推关系等。关于这些函数,导出了两个新的正交投影及其误差界限。此外,还引入了两个新的 Müntz 型正交规则。作为这些基函数的两个应用,一些分数常微分方程和偏微分方程被考虑并给出了数值结果。
更新日期:2021-06-24
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