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

Ishtiaq, Umar; Jahangeer, Fahad; Kattan, Doha A.; Argyros, Ioannis K.; Regmi, Samundra

doi:10.3390/axioms12080725

Open AccessArticle

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

by

Umar Ishtiaq

¹

,

Fahad Jahangeer

²,

Doha A. Kattan

³

,

Ioannis K. Argyros

^4,*

and

Samundra Regmi

⁵

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

^*

Author to whom correspondence should be addressed.

Axioms 2023, 12(8), 725; https://doi.org/10.3390/axioms12080725

Submission received: 8 June 2023 / Revised: 21 July 2023 / Accepted: 24 July 2023 / Published: 26 July 2023

(This article belongs to the Special Issue Imprecision to Insights: Theoretical Advances in Fuzzy Uncertainty Modeling and Their Applications in New Frontiers)

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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] \to (- \infty, \infty)

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.

Keywords: fixed point; fuzzy metric spaces; (ℐ,

S

)-fuzzy iterative mappings; fractional differential equations fixed point; fuzzy metric spaces; (ℐ,

S

)-fuzzy iterative mappings; fractional differential equations

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MDPI and ACS Style

Ishtiaq, U.; Jahangeer, F.; Kattan, D.A.; Argyros, I.K.; Regmi, S. On Orthogonal Fuzzy Interpolative Contractions with Applications to Volterra Type Integral Equations and Fractional Differential Equations. Axioms 2023, 12, 725. https://doi.org/10.3390/axioms12080725

AMA Style

Ishtiaq U, Jahangeer F, Kattan DA, Argyros IK, Regmi S. On Orthogonal Fuzzy Interpolative Contractions with Applications to Volterra Type Integral Equations and Fractional Differential Equations. Axioms. 2023; 12(8):725. https://doi.org/10.3390/axioms12080725

Chicago/Turabian Style

Ishtiaq, Umar, Fahad Jahangeer, Doha A. Kattan, Ioannis K. Argyros, and Samundra Regmi. 2023. "On Orthogonal Fuzzy Interpolative Contractions with Applications to Volterra Type Integral Equations and Fractional Differential Equations" Axioms 12, no. 8: 725. https://doi.org/10.3390/axioms12080725

APA Style

Ishtiaq, U., Jahangeer, F., Kattan, D. A., Argyros, I. K., & Regmi, S. (2023). On Orthogonal Fuzzy Interpolative Contractions with Applications to Volterra Type Integral Equations and Fractional Differential Equations. Axioms, 12(8), 725. https://doi.org/10.3390/axioms12080725

Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details here.

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

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