Ozarslan Ramazan, Bas Erdal, Baleanu Dumitru
Department of Mathematics, Science Faculty, Firat University, 23119 Elazig, Turkey.
Department of Mathematics and Computer Sciences, Faculty of Arts and Sciences, Cankaya University, 06790 Ankara, Turkey.
Chaos. 2020 Mar;30(3):033137. doi: 10.1063/1.5131167.
We analyze fractional Sturm-Liouville problems with a new generalized fractional derivative in five different forms. We investigate the representation of solutions by means of ρ-Laplace transform for generalized fractional Sturm-Liouville initial value problems. Finally, we examine eigenfunctions and eigenvalues for generalized fractional Sturm-Liouville boundary value problems. All results obtained are compared with simulations in detail under different α fractional orders and real ρ values.
我们用五种不同形式的新型广义分数阶导数分析分数阶斯特姆 - 刘维尔问题。我们研究广义分数阶斯特姆 - 刘维尔初值问题解的ρ - 拉普拉斯变换表示。最后，我们研究广义分数阶斯特姆 - 刘维尔边值问题的特征函数和特征值。在不同的α分数阶和实ρ值下，将所有得到的结果与模拟进行详细比较。
