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Research Article | Open Access

Fixed point results with applications to nonlinear fractional differential equations

Saleh Abdullah Al-Mezel1,2, Jamshaid Ahmad2( )
Industrial Area, Majmaah University, Al Majma'ah 15341, Saudi Arabia
Department of Mathematics, University of Jeddah, P. O. Box 80327, Jeddah 21589, Saudi Arabia
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Abstract

The aim of this paper is to define a Berinde type ( ρ, μ)- ϑ contraction and establish some fixed point results for self mappings in the setting of complete metric spaces. We derive new fixed point results, which extend and improve some results in the literature. We also supply a non trivial example to support the obtained results. Finally, we investigate the existence of solutions for the nonlinear fractional differential equation.

Keywords

nonlinear fractional differential equationBerinde type (ρ, μ)-ϑ contractionscomplete metric spacesfixed point
CLC number: 46S40, 47H10, 54H25

References

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AIMS Mathematics
Volume 8 Issue 8,
August 2023
Pages 19743-19756
DOI: 10.3934/math.20231006

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Al-Mezel SA, Ahmad J. Fixed point results with applications to nonlinear fractional differential equations. AIMS Mathematics, 2023, 8(8): 19743-19756. https://doi.org/10.3934/math.20231006

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Received: 31 December 2022
Revised: 18 February 2023
Accepted: 21 February 2023
Published: 15 August 2023
©2023 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)