Stability analysis and solutions of fractional boundary value problem on the cyclopentasilane graph

Guotao Wang; Hualei Yuan; Dumitru Baleanu

doi:10.1016/j.heliyon.2024.e32411

Stability analysis and solutions of fractional boundary value problem on the cyclopentasilane graph

Heliyon. 2024 Jun 10;10(12):e32411. doi: 10.1016/j.heliyon.2024.e32411. eCollection 2024 Jun 30.

Authors

Guotao Wang¹, Hualei Yuan¹, Dumitru Baleanu^{2

3}

Affiliations

¹ School of Mathematics and Computer Science, Shanxi Normal University, Taiyuan, Shanxi 030031, China.
² Department of Mathematics, Faculty of Art and Sciences, Cankaya University, Balgat, 06530, Ankara, Turkey.
³ Institute of Space Sciences, Magurele-Bucharest, Romania.

Abstract

The study is being applied to a model involving silane and on cyclopentasilane graph. We consider a graph with labeled vertices by 0 or 1 inspired by the molecular structure of cyclopentasilane. In this paper, we first study the existence of solutions to fractional conformable boundary value problem on the cyclopentasilane graph by applying Scheafer and Krasnoselskii fixed point theorems. Furthermore, we investigate different kinds of Ulam stability such as Ulam-Hyers stable, generalized Ulam-Hyers stable, Ulam-Hyers-Rassias stable and generalized Ulam-Hyers-Rassias stable for the given problem. Finally, we give an example to support our important results.

Keywords: Cyclopentasilane graph; Existence; Fixed point theorem; Fractional conformable derivative; Ulam stability.