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 | Zendy

Vaibhav Mehandiratta | Zendy; Mani Mehra | Zendy; Günter Leugering | Zendy

Open Access

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

Author(s) -

Vaibhav Mehandiratta,

Mani Mehra,

Günter Leugering

Publication year - 2021

Publication title -

networks and heterogeneous media

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.732

H-Index - 34

eISSN - 1556-181X

pISSN - 1556-1801

DOI - 10.3934/nhm.2021003

Subject(s) - mathematics , contraction principle , uniqueness , fixed point theorem , banach fixed point theorem , contraction mapping , nonlinear system , boundary value problem , fractional calculus , graph , mathematical analysis , discrete mathematics , physics , quantum mechanics

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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