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.
Highlights
Introduction and preliminariesWhat mathematics needs today is various applications to improve the standard of living of humanity
5 Conclusion More natural phenomena and processes in the world are modeled by different types of fractional differential equations
By using the technique of α-admissible α-ψ-contractions, we study a fractional hybrid version of the Sturm–Liouville equation
Summary
Introduction and preliminariesWhat mathematics needs today is various applications to improve the standard of living of humanity. Many researchers are currently studying various types of advanced mathematical modeling using fractional differential equations and its related inclusion version with more general boundary value conditions. Many papers have been published on the existence of solutions for different fractional boundary value problems (see, for example, [18–34]).
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