Application of fixed point result to solve integral equation in the setting of graphical Branciari $ {\aleph } $-metric spaces

Rajagopalan Ramaswamy; Gunaseelan Mani; Rajagopalan Ramaswamy; Gunaseelan Mani

doi:10.3934/math.20241576

AIMS Mathematics

2024, Volume 9, Issue 11: 32945-32961. doi: 10.3934/math.20241576

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Application of fixed point result to solve integral equation in the setting of graphical Branciari $ {\aleph } $-metric spaces

Rajagopalan Ramaswamy ^{1
,
,},
Gunaseelan Mani ²

1.
Department of Mathematics, College of Science and Humanities in Alkharj, Prince Sattam Bin Abdulaziz University, Alkharj 11942, Saudi Arabia
2.
Department of Mathematics, Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences, Chennai 602 105, Tamil Nadu, India

Received: 12 September 2024 Revised: 04 November 2024 Accepted: 11 November 2024 Published: 21 November 2024
MSC : 47H10, 54H25

In this present paper, we introduce graphical Branciari $ \aleph $-metric space and prove the fixed point theorem for $ \varOmega $-$ \mathcal{Q} $-contraction on complete graphical Branciari $ \aleph $ -metric spaces. Our result has been supplemented with suitable, non trivial examples. We have applied the derived fixed point result to solve non-linear Fredholm integral equations and fractional differential equation.
Citation: Rajagopalan Ramaswamy, Gunaseelan Mani. Application of fixed point result to solve integral equation in the setting of graphical Branciari $ {\aleph } $-metric spaces[J]. AIMS Mathematics, 2024, 9(11): 32945-32961. doi: 10.3934/math.20241576

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Abstract

In this present paper, we introduce graphical Branciari $ \aleph $-metric space and prove the fixed point theorem for $ \varOmega $-$ \mathcal{Q} $-contraction on complete graphical Branciari $ \aleph $ -metric spaces. Our result has been supplemented with suitable, non trivial examples. We have applied the derived fixed point result to solve non-linear Fredholm integral equations and fractional differential equation.

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