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Research Article | Open Access

Solving a fractional differential equation via θ -contractions in ℜ-complete metric spaces

Khalil Javed1, Muhammad Arshad1, Amani S. Baazeem2, Nabil Mlaiki3( )
Department of Mathematics & Statistics, International Islamic University, H-10 Islamabad 44000, Pakistan
Department of Mathematics and Statistics, College of Science, IMSIU (Imam Mohammed Ibn Saud Islamic University), P.O. Box 90950, Riyadh 11623, Saudi Arabia
Department of Mathematics and Sciences, Prince Sultan University, P.O. Box 66833, Riyadh 11586, Saudi Arabia
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Abstract

In this manuscript, we introduce the notion of ℜ α- θ-contractions and prove some fixed-point theorems in the sense of ℜ-complete metric spaces. These results generalize existing ones in the literature. Also, we provide some illustrative non-trivial examples and applications to a non-linear fractional differential equation.

Keywords

ℜ-metric spacefixed point resultsnon-linear fractional differential equation
CLC number: 47H10, 54H25

References

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AIMS Mathematics
Volume 7 Issue 9,
September 2022
Pages 16869-16888
DOI: 10.3934/math.2022926

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Cite this article:
Javed K, Arshad M, Baazeem AS, et al. Solving a fractional differential equation via θ -contractions in ℜ-complete metric spaces. AIMS Mathematics, 2022, 7(9): 16869-16888. https://doi.org/10.3934/math.2022926

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Received: 06 June 2022
Revised: 06 July 2022
Accepted: 06 July 2022
Published: 15 September 2022
©2022 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)