Existence of solutions for a class of nonlinear boundary value problems on the hexasilinane graph

Turab, Ali; Mitrović, Zoran D.; Savić, Ana

doi:10.1186/s13662-021-03653-w

Cited by 13 publications

(5 citation statements)

References 20 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In such studies, the authors utilized the concept of a star graph, which has only one junction node (see Fig 1). Since then, various authors have used notable methods to extend the problem in different directions see [33][34][35][36][37][38] and the references within.…”

Section: Introductionmentioning

confidence: 99%

A unified fixed point approach to study the existence of solutions for a class of fractional boundary value problems arising in a chemical graph theory

Sintunavarat

Turab

2022

PLoS ONE

Self Cite

View full text Add to dashboard Cite

A theory of chemical graphs is a part of mathematical chemistry concerned with the effects of connectedness in chemical graphs. Several researchers have studied the solutions of fractional differential equations using the concept of star graphs. They employed star graphs because their technique requires a central node with links to adjacent vertices but no edges between nodes. The purpose of this paper is to extend the method’s range by introducing the concept of an octane graph, which is an essential organic compound having the formula C8H18. In this manner, we analyze a graph with vertices annotated by 0 or 1, which is influenced by the structure of the chemical substance octane, and formulate a fractional boundary value problem on each of the graph’s edges. We use the Schaefer and Krasnoselskii fixed point theorems to investigate the existence of solutions to the presented boundary value problems in the framework of the Caputo fractional derivative. Finally, two examples are provided to highlight the importance of our results in this area of study.

show abstract

Section: Introductionmentioning

confidence: 99%

A unified fixed point approach to study the existence of solutions for a class of fractional boundary value problems arising in a chemical graph theory

Sintunavarat

Turab

2022

PLoS ONE

Self Cite

View full text Add to dashboard Cite

show abstract

“…Although only a tiny amount of work has been dedicated to the topic, using fixed point theory approaches (see [28,29]), it has been proven that solutions exist for boundary value issues involving star graphs (see Figure 2). One can see the most up-to-date research in this area in which the authors use different types of graphs (i.e., ethane [30,31], glucose [32], methylpropane [33], hexasilinane [34], cyclohexane [35], octane [36], etc.) and defined the differential equations on their edges.…”

Section: Introductionmentioning

confidence: 99%

Study of Fractional Differential Equations Emerging in the Theory of Chemical Graphs: A Robust Approach

Turab

Rosli

2022

Mathematics

View full text Add to dashboard Cite

The study of the interconnections between chemical systems is known as chemical graph theory. Through the use of star graphs, a limited group of researchers has examined the space of possible solutions for boundary-value problems. They recognized that for their strategy to function, they needed a core node related to other nodes but not to itself; as a result, they opted to use star graphs. In this sense, the graphs of neopentane will be helpful in extending the scope of our technique. It has the CAS number 463-82-1 and the chemical formula C5H12, and it is a component of a petrochemical precursor. In order to determine whether or not the suggested boundary-value problems on these graphs have any known solutions, we use the theorems developed by Schaefer and Krasnoselskii on fixed points. In addition, we illustrate our preliminary results with the help of an example that we present.

show abstract

“…In 2021, Turab et al [16] looked into the existence of solutions for a class of nonlinear boundary value problems on a hexasilinane graph with applications in chemical formulas. The authors in [17] dealt with the existence and Ulam-Hyers stability (UHs) of Caputo-type fuzzy fractional differential equations (FFDEs) with time-delays by applying Schauder's fixed point theorem and a hypothetical condition.…”

Section: Introductionmentioning

confidence: 99%

On the Boundary Value Problem of Nonlinear Fractional Integro-Differential Equations

Saadati

Srivastava

et al. 2022

Mathematics

View full text Add to dashboard Cite

Using Banach’s contractive principle and the Laray–Schauder fixed point theorem, we study the uniqueness and existence of solutions to a nonlinear two-term fractional integro-differential equation with the boundary condition based on Babenko’s approach and the Mittag–Leffler function. The current work also corrects major errors in the published paper dealing with a one-term differential equation. Furthermore, we provide examples to illustrate the application of our main theorems.

show abstract

Existence of solutions for a class of nonlinear boundary value problems on the hexasilinane graph

Cited by 13 publications

References 20 publications

A unified fixed point approach to study the existence of solutions for a class of fractional boundary value problems arising in a chemical graph theory

A unified fixed point approach to study the existence of solutions for a class of fractional boundary value problems arising in a chemical graph theory

Study of Fractional Differential Equations Emerging in the Theory of Chemical Graphs: A Robust Approach

On the Boundary Value Problem of Nonlinear Fractional Integro-Differential Equations

Contact Info

Product

Resources

About