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Multivalued problems via orthogonal contraction mappings with application to fractional differential equation

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Abstract

In this manuscript, we give a partial answer to Reich’s problem on multivalued contraction mappings and generalize Mizoguchi–Takahashi’s fixed point theorem using a new approach of multivalued orthogonal \((\tau ,F)\)-contraction mappings in the framework of orthogonal metric spaces. We give a nontrivial example to prove the validity of our results. Some interesting consequences are also deduced. Finally, as application, we prove the existence and uniqueness of the solution of a nonlinear fractional differential equation.

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Acknowledgements

The authors are thankful to the editor and anonymous referee for valuable suggestions. The first author (Sumit Chandok) is thankful to the NBHM-DAE for the research project 02011/11/2020/NBHM(RP)/R&D-II/7830.

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Authors and Affiliations

  1. School of Mathematics, Thapar Institute of Engineering and Technology, Patiala, Punjab, 147004, India

    Sumit Chandok & R. K. Sharma

  2. Faculty of Mechanical Engineering, University of Belgrade, Kraljice Marije 16, 11120, Beograd 35, Serbia

    Stojan Radenović

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  1. Sumit Chandok
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  2. R. K. Sharma
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  3. Stojan Radenović
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Correspondence to Sumit Chandok.

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Chandok, S., Sharma, R.K. & Radenović, S. Multivalued problems via orthogonal contraction mappings with application to fractional differential equation. J. Fixed Point Theory Appl. 23, 14 (2021). https://doi.org/10.1007/s11784-021-00850-8

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  • DOI: https://doi.org/10.1007/s11784-021-00850-8

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