On a fractional hybrid version of the Sturm–Liouville equation

• Main Authors: Zohreh Zeinalabedini Charandabi, Shahram Rezapour, Mina Ettefagh
• Format: Article
• Language: English
• Published: SpringerOpen 2020-06-01
• Series: Advances in Difference Equations
• Subjects: α-ψ-contraction; Fractional hybrid version; Multi-point boundary value conditions; Sturm–Liouville equation
• Online Access: http://link.springer.com/article/10.1186/s13662-020-02765-z

Abstract 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.