A Theoretical Analysis of a Fractional Multi-Dimensional System of Boundary Value Problems on the Methylpropane Graph via Fixed Point Technique

Shahram Rezapour, Chernet Tuge Deressa, Azhar Hussain, Sina Etemad, Reny George and Bashir Ahmad
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Shahram Rezapour: Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz 751-71379, Iran
Chernet Tuge Deressa: Department of Mathematics, College of Natural Sciences, Jimma University, Jimma, Ethiopia
Azhar Hussain: Department of Mathematics, University of Sargodha, Sargodha 40100, Pakistan
Sina Etemad: Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz 751-71379, Iran
Reny George: Department of Mathematics, College of Science and Humanities in AlKharj, Prince Sattam Bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia
Bashir Ahmad: Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia

Mathematics, 2022, vol. 10, issue 4, 1-26

Abstract: Few studies have investigated the existence and uniqueness of solutions for fractional differential equations on star graphs until now. The published papers on the topic are based on the assumption of existence of one junction node and some boundary nodes as the origin on a star graph. These structures are special cases and do not cover more general non-star graph structures. In this paper, we state a labeling method for graph vertices, and then we prove the existence results for solutions to a new family of fractional boundary value problems (FBVPs) on the methylpropane graph. We design the chemical compound of the methylpropane graph with vertices specified by 0 or 1, and on every edge of the graph, we consider fractional differential equations. We prove the existence of solutions for the proposed FBVPs by means of the Krasnoselskii’s and Scheafer’s fixed point theorems, and further, we study the Ulam–Hyers type stability for the given multi-dimensional system. Finally, we provide an illustrative example to examine our results.

Keywords: fractional differential equation; boundary value problem; methylpropane graph; the Caputo fractional derivative; stability (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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