2021
DOI: 10.3934/nhm.2021003
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Existence results and stability analysis for a nonlinear fractional boundary value problem on a circular ring with an attached edge : A study of fractional calculus on metric graph

Abstract: In this paper, we study a nonlinear fractional boundary value problem on a particular metric graph, namely, a circular ring with an attached edge. First, we prove existence and uniqueness of solutions using the Banach contraction principle and Krasnoselskii's fixed point theorem. Further, we investigate different kinds of Ulam-type stability for the proposed problem. Finally, an example is given in order to demonstrate the application of the obtained theoretical results.

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Cited by 15 publications
(5 citation statements)
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“…Given its wide-ranging applications, studying graphs holds significant meaning. In recent years, significant progress has been made in both theoretical and practical aspects in the study of fractional differential equations on graphs [16][17][18][19][20][21][22][23]. Numerous scholars have dedicated their efforts to exploring mathematical models on graphs, describing them through ordinary differential equations or fractional differential equations.…”
Section: Introductionmentioning
confidence: 99%
See 2 more Smart Citations
“…Given its wide-ranging applications, studying graphs holds significant meaning. In recent years, significant progress has been made in both theoretical and practical aspects in the study of fractional differential equations on graphs [16][17][18][19][20][21][22][23]. Numerous scholars have dedicated their efforts to exploring mathematical models on graphs, describing them through ordinary differential equations or fractional differential equations.…”
Section: Introductionmentioning
confidence: 99%
“…A study was conducted by Mehandiratta et al [16] in 2021, focusing on fractional calculus applied to metric graph. The researchers examined a nonlinear fractional boundary value problem on a graph that included cycles (see Figure 1), and they successfully obtained results related to its existence and stability analysis:…”
Section: Introductionmentioning
confidence: 99%
See 1 more Smart Citation
“…Then they established existence and uniqueness results by a fixed point theory. This work was extended to the existence and uniqueness of solutions of a nonlinear fractional boundary value problem on a circular ring with an attached edge in [28] by the same authors. The results are achieved by the Banach contraction principle and Krasnoselskii's fixed point theorem.…”
Section: Introduction and Problem Settingmentioning
confidence: 99%
“…Then they established existence and uniqueness results by a fixed point theory. This work was extended to the existence and uniqueness of solutions of a nonlinear fractional boundary value problem on a circular ring with an attached edge in [31] by the same authors. The results are achieved by the Banach contraction principle and Krasnoselskii's fixed point theorem.…”
mentioning
confidence: 99%