Fixed Point Theorems in Controlled Rectangular Modular Metric Spaceswith Solution of Fractional Differential Equations

Authors

  • Umar Ishtiaq Office of Research, Innovation and Commercialization, University of Management and Technology, Lahore 54770, Pakistan
  • Naeem Saleem Department of Mathematics, University of Management and Technology, Lahore, Pakistan
  • Muhammad Farhan Department of Mathematics, Numl University Multan Campus, Multan, Pakistan
  • Maggie Aphne Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, Ga-Rankuwa, Pretoria, Medunsa-0204, South Africa
  • Mohammad Showkat Rahim Chowdhury Department of Mathematics and Statistics, The University of Lahore, Lahore, Pakistan

DOI:

https://doi.org/10.29020/nybg.ejpam.v18i1.5794

Keywords:

modular metric space, existence and uniqueness, non-linear fractional differential equations, Controlled metric space

Abstract

In this paper, we establish the notion of controlled rectangular modular metric space as a generalization of modular $b-$metric space and rectangular $b-$metric space. We used contraction mappings to find the existence and uniqueness of a fixed point in the framework of controlled rectangular modular metric space. We give several non-trivial examples and show the validity of contraction mappings via graphs. At the end, we utilize our main result to solve a non-linear fractional differential equation.

Author Biography

  • Naeem Saleem, Department of Mathematics, University of Management and Technology, Lahore, Pakistan

    Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences
    University, Ga-Rankuwa, Pretoria, Medunsa-0204, South Africa

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Published

2025-01-31

Issue

Vol. 18 No. 1: (January 2025)

Section

Nonlinear Analysis

License

Copyright (c) 2025 Umar Ishtiaq, Naeem Saleem, Muhammad Farhan, Maggie Aphne, Mohammad Showkat Rahim Chowdhury

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How to Cite

Fixed Point Theorems in Controlled Rectangular Modular Metric Spaceswith Solution of Fractional Differential Equations. (2025). European Journal of Pure and Applied Mathematics, 18(1), 5794. https://doi.org/10.29020/nybg.ejpam.v18i1.5794