论文标题
关于一致的分数Legendre多项式及其与应用的收敛性
On conformable fractional Legendre polynomials and their convergence properties with applications
论文作者
论文摘要
本文的主要目的是对符合符合的分数Legendre多项式（CFLP）进行广泛的研究。这项研究被认为是标量案例的一种概括性和完善性，使得符合分数分化的背景。我们通过不同的生成功能介绍了CFLP，并提供了一些主要属性和收敛结果。随后，某些纯粹的复发和差异复发关系，拉普拉斯的第一个积分公式和正交特性然后为CFLP开发。我们将研究以呈现的CFLP呈现，并使用搭配方法描述适用的方案，以解决符合衍生物的意义上解决某些分数微分方程（FDE）。对FDE的一些有用的例子进行了处理，以支持我们的理论结果并检查其确切的解决方案。据我们所知，获得的结果是新提出的，可以丰富特殊功能的分数理论。
The main objective of this paper is to give a wide study on the conformable fractional Legendre polynomials (CFLPs). This study is assumed to be a generalization and refinement, in an easy way, of the scalar case into the context of the conformable fractional differentiation. We introduce the CFLPs via different generating functions and provide some of their main properties and convergence results. Subsequently, some pure recurrence and differential recurrence relations, Laplace's first integral formula and orthogonal properties are then developed for CFLPs. We append our study with presenting shifted CFLPs and describing applicable scheme using the collocation method to solve some fractional differential equations (FDEs) in the sense of conformable derivative. Some useful examples of FDEs are treated to support our theoretical results and examining their exact solutions. To the best of our knowledge, the obtained results are newly presented and could enrich the fractional theory of special functions.
