On some conformable boundary value problems in the setting of a new generalized conformable fractional derivative

IF 2 3区数学 Q1 MATHEMATICS

Demonstratio Mathematica Pub Date : 2023-01-01 DOI:10.1515/dema-2022-0212

M. Vivas-Cortez, Martin Patricio Árciga, Juan Carlos Najera, J. E. Hernández

引用次数: 2

Abstract

Abstract The fundamental objective of this article is to investigate about the boundary value problem with the uses of a generalized conformable fractional derivative introduced by Zarikaya et al. (On generalized the conformable calculus, TWMS J. App. Eng. Math. 9 (2019), no. 4, 792–799, http://jaem.isikun.edu.tr/web/images/articles/vol.9.no.4/11.pdf). In the development of the this article, by using classical methods of fractional calculus, we find a definition of the generalized fractional Wronskian according to the fractional differential operator defined by Zarikaya, a fractional version of the Sturm-Picone theorem, and in addition, the stability criterion given by the Hyers-Ulam theorem is studied with the use of the aforementioned fractional derivatives.

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关于一个新的广义保形分数导数设置中的一些保形边值问题

摘要本文的基本目的是使用Zarikaya等人引入的广义保形分数导数来研究边值问题。（关于广义保形微积分，TWMS J.App.Eng.Math.9（2019），no.4792-799，http://jaem.isikun.edu.tr/web/images/articles/vol.9.no.4/11.pdf)。在本文的发展过程中，利用分数微积分的经典方法，我们根据Zarikaya定义的分数微分算子，Sturm-Picone定理的分数版本，找到了广义分数Wronskian的定义，此外，利用上述分数阶导数研究了Hyers-Ulam定理给出的稳定性判据。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Demonstratio Mathematica MATHEMATICS-

CiteScore

2.40

自引率

5.00%

发文量

审稿时长

35 weeks

期刊介绍： Demonstratio Mathematica publishes original and significant research on topics related to functional analysis and approximation theory. Please note that submissions related to other areas of mathematical research will no longer be accepted by the journal. The potential topics include (but are not limited to): -Approximation theory and iteration methods- Fixed point theory and methods of computing fixed points- Functional, ordinary and partial differential equations- Nonsmooth analysis, variational analysis and convex analysis- Optimization theory, variational inequalities and complementarity problems- For more detailed list of the potential topics please refer to Instruction for Authors. The journal considers submissions of different types of articles. "Research Articles" are focused on fundamental theoretical aspects, as well as on significant applications in science, engineering etc. “Rapid Communications” are intended to present information of exceptional novelty and exciting results of significant interest to the readers. “Review articles” and “Commentaries”, which present the existing literature on the specific topic from new perspectives, are welcome as well.