On Orthogonal Fuzzy Interpolative Contractions with Applications to Volterra Type Integral Equations and Fractional Differential Equations-Reference-Cited by-同舟云学术

On Orthogonal Fuzzy Interpolative Contractions with Applications to Volterra Type Integral Equations and Fractional Differential Equations

Published:2023-07-26 Issue:8 Volume:12 Page:725
ISSN:2075-1680
Container-title:Axioms
language:en
Short-container-title:Axioms

Author:

Ishtiaq Umar¹^ORCID,Jahangeer Fahad²,Kattan Doha A.³^ORCID,Argyros Ioannis K.⁴^ORCID,Regmi Samundra⁵^ORCID

Affiliation:

1. Office of Research, Innovation and Commercialization, University of Management and Technology, Lahore 54770, Pakistan

2. Department of Mathematics and Statistics, International Islamic University Islamabad, Islamabad 44000, Pakistan

3. Department of Mathematics, Faculty of Sciences and Arts, King Abdulaziz University, Rabigh 25712, Saudi Arabia

4. Department of Computing and Mathematical Sciences, Cameron University, Lawton, OK 73505, USA

5. Department of Mathematics, University of Houston, Houston, TX 77204, USA

Abstract

In this paper, orthogonal fuzzy versions are reported for some celebrated iterative mappings. We provide various concrete conditions on the real valued functions J,S:(0,1]→(−∞,∞) for the existence of fixed-points of (J,S)-fuzzy interpolative contractions. This way, many fixed point theorems are developed in orthogonal fuzzy metric spaces. We apply the (J,S)-fuzzy version of Banach fixed point theorem to demonstrate the existence and uniqueness of the solution. These results are supported with several non-trivial examples and applications to Volterra-type integral equations and fractional differential equations.

Publisher

MDPI AG

Subject

Geometry and Topology,Logic,Mathematical Physics,Algebra and Number Theory,Analysis

Link

https://www.mdpi.com/2075-1680/12/8/725/pdf

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