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Fixed Point Results for $\alpha$-Type $F$-Suzuki Contraction and $\alpha$-Type $F$-Weak-Suzuki Contraction With Application to Non-linear Fractional Differential Equation in $b$-Metric Spaces
Version 1
: Received: 11 December 2023 / Approved: 13 December 2023 / Online: 13 December 2023 (10:05:40 CET)
How to cite:
Gher, Y.T.; Tola, K.K.; Yesuf, H.E. Fixed Point Results for $\alpha$-Type $F$-Suzuki Contraction and $\alpha$-Type $F$-Weak-Suzuki Contraction With Application to Non-linear Fractional Differential Equation in $b$-Metric Spaces. Preprints2023, 2023120963. https://doi.org/10.20944/preprints202312.0963.v1
Gher, Y.T.; Tola, K.K.; Yesuf, H.E. Fixed Point Results for $\alpha$-Type $F$-Suzuki Contraction and $\alpha$-Type $F$-Weak-Suzuki Contraction With Application to Non-linear Fractional Differential Equation in $b$-Metric Spaces. Preprints 2023, 2023120963. https://doi.org/10.20944/preprints202312.0963.v1
Gher, Y.T.; Tola, K.K.; Yesuf, H.E. Fixed Point Results for $\alpha$-Type $F$-Suzuki Contraction and $\alpha$-Type $F$-Weak-Suzuki Contraction With Application to Non-linear Fractional Differential Equation in $b$-Metric Spaces. Preprints2023, 2023120963. https://doi.org/10.20944/preprints202312.0963.v1
APA Style
Gher, Y.T., Tola, K.K., & Yesuf, H.E. (2023). Fixed Point Results for $\alpha$-Type $F$-Suzuki Contraction and $\alpha$-Type $F$-Weak-Suzuki Contraction With Application to Non-linear Fractional Differential Equation in $b$-Metric Spaces. Preprints. https://doi.org/10.20944/preprints202312.0963.v1
Chicago/Turabian Style
Gher, Y.T., Kidane Koyas Tola and Haider Ebrahim Yesuf. 2023 "Fixed Point Results for $\alpha$-Type $F$-Suzuki Contraction and $\alpha$-Type $F$-Weak-Suzuki Contraction With Application to Non-linear Fractional Differential Equation in $b$-Metric Spaces" Preprints. https://doi.org/10.20944/preprints202312.0963.v1
Abstract
In this work, we introduce a new concepts for $\alpha$-type $F$-Suzuki contraction and $\alpha$-type $F$-weak-Suzuki contraction in the context of $b$-metric spaces. Compared to the $\alpha$-type $F$-contraction and $F$-Suzuki contraction mappings, these contractions are essentially weaker. For these type of contraction mappings, sufficient conditions are established for the fixed point's existence and uniqueness in $b$-metric spaces. As a result, the findings encompass several generalizations. To show the usability of our obtained results, we provide a supportive example and an application to a non-linear differential equation with fractional order.
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
