Existence solution of a system of differential equations using generalized Darbo's fixed point theorem

Rahul; Nihar Kumar Mahato; Rahul; Nihar Kumar Mahato

doi:10.3934/math.2021773

AIMS Mathematics

2021, Volume 6, Issue 12: 13358-13369. doi: 10.3934/math.2021773

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Research article

Existence solution of a system of differential equations using generalized Darbo's fixed point theorem

Rahul ,
Nihar Kumar Mahato ^,

Discipline of Natural Science, PDPM Indian Institute of Information Technology, Design, and Manufacturing Jabalpur, India

Received: 22 April 2021 Accepted: 19 August 2021 Published: 16 September 2021
MSC : 47H08, 47H10

In this paper, we proposed a generalized of Darbo's fixed point theorem via the concept of operators $ S(\bullet; .) $ associated with the measure of noncompactness. Using this generalized Darbo fixed point theorem, we have given the existence of solution of a system of differential equations. At the end, we have given an example which supports our findings.
- measure of noncompactness(MNC),
- triple fixed point(TFP),
- condensing operator,
- differential equations,
- concept of operators
Citation: Rahul, Nihar Kumar Mahato. Existence solution of a system of differential equations using generalized Darbo's fixed point theorem[J]. AIMS Mathematics, 2021, 6(12): 13358-13369. doi: 10.3934/math.2021773

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Abstract

In this paper, we proposed a generalized of Darbo's fixed point theorem via the concept of operators $ S(\bullet; .) $ associated with the measure of noncompactness. Using this generalized Darbo fixed point theorem, we have given the existence of solution of a system of differential equations. At the end, we have given an example which supports our findings.

References

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