Solving a fractional differential equation via $ {\theta } $-contractions in ℜ-complete metric spaces

Khalil Javed; Muhammad Arshad; Amani S. Baazeem; Nabil Mlaiki; Khalil Javed; Muhammad Arshad; Amani S. Baazeem; Nabil Mlaiki

doi:10.3934/math.2022926

AIMS Mathematics

2022, Volume 7, Issue 9: 16869-16888. doi: 10.3934/math.2022926

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Solving a fractional differential equation via $ {\theta } $-contractions in ℜ-complete metric spaces

1.
Department of Mathematics & Statistics, International Islamic University, H-10 Islamabad 44000, Pakistan
2.
Department of Mathematics and Statistics, College of Science, IMSIU (Imam Mohammed Ibn Saud Islamic University), P.O. Box 90950, Riyadh 11623, Saudi Arabia
3.
Department of Mathematics and Sciences, Prince Sultan University, P.O. Box 66833, Riyadh 11586, Saudi Arabia

Received: 06 June 2022 Revised: 06 July 2022 Accepted: 06 July 2022 Published: 15 July 2022
MSC : 47H10, 54H25

In this manuscript, we introduce the notion of ℜ$ \alpha $-$ \theta $-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.
- ℜ-metric space,
- fixed point results,
- non-linear fractional differential equation
Citation: Khalil Javed, Muhammad Arshad, Amani S. Baazeem, Nabil Mlaiki. Solving a fractional differential equation via $ {\theta } $-contractions in ℜ-complete metric spaces[J]. AIMS Mathematics, 2022, 7(9): 16869-16888. doi: 10.3934/math.2022926

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Abstract

In this manuscript, we introduce the notion of ℜ$ \alpha $-$ \theta $-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.

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