Fixed point results for multivalued $(\alpha,\mathcal{F})$-contractions on $S$-metric spaces with applications

Authors

Gurucharan Singh Saluja Rtd. Prof. of Mathematics, Govt. P.G. College Jagdalpur (Chhattisgarh), India.

Keywords:

Fixed point, multivalued $(\alpha,\mathcal{F})$-contraction, $\alpha$-admissible mapping, $S$-metric space.

Abstract

In this paper, we obtain some fixed point results involving $\alpha$-admissibility for multi-valued $\mathcal{F}$-contractions in the framework of complete $S$-metric spaces. Appropriate illustrations are provided to support the main results. Finally, an application is developed by demonstrating the existence of a solution to an integral equation. Also, as an application, we establish the existence and uniqueness of the solutions to differential equations in the framework of fractional derivatives involving Mittag-Leffler kernals via the fixed point technique. Our results extend and generalize many well-known results in the existing literature.

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