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2021, Volume 16, Issue 2: 155-185. 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

1.
Department of Mathematics, Indian Institute of Technology Delhi, 110016, Delhi, India
2.
Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), Lehrstuhl Angewandte Mathematik II, Cauerstr. 11, 91058 Erlangen, Germany

^* Corresponding author: Mani Mehra
^* Corresponding author: Mani Mehra

Received: July 2020

Revised: November 2020

Early access: January 2021

Published: June 2021

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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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Mathematics Subject Classification: Primary: 34A08, 34B15, 26A33; Secondary: 34D20.

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Figure 1. A general star graph with k edges and k+1 vertices

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Figure 2. A circular ring with an attached edge

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