On a fractional hybrid version of the Sturm–Liouville equation

Advances in Difference Equations

article

Charandabi, Zohreh Zeinalabedini¹  Rezapour, Shahram²  Ettefagh, Mina⁵ 

[1] Department of Mathematics, Sarab Branch, Islamic Azad University;Institute of Research and Development, Duy Tan University;Department of Medical Research, China Medical University Hospital, China Medical University;Department of Mathematics, Azarbaijan Shahid Madani University;Department of Mathematics, Tabriz Branch, Islamic Azad University

关键词: α;    ψ -contraction;    Fractional hybrid version;    Multi-point boundary value conditions;    Sturm–Liouville equation;   

DOI  :  10.1186/s13662-020-02765-z

学科分类：航空航天科学

来源: SpringerOpen

【 摘 要 】

It is well known that the Sturm–Liouville equation has many applications in different areas of science. Thus, it is important to review different versions of the well-known equation. The technique of α-admissible α-ψ-contractions was introduced by Samet et al. in (Nonlinear Anal. 75:2154–2165, 2012). Our aim in this work is to study a fractional hybrid version of the Sturm–Liouville equation by mixing the technique of Samet. In fact, by using the technique of α-admissible α-ψ-contractions, we investigate the existence of solutions for the fractional hybrid Sturm–Liouville equation by using the multi-point boundary value conditions. Also, we review the existence of solutions for a fractional hybrid version of the problem under the integral boundary value conditions. Finally, we provide two examples to illustrate our main results.

【 授权许可】

CC BY