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Second Order Iterative Dynamic Boundary Value Problems with Mixed Derivative Operators with Applications

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Abstract

In this paper, we derive sufficient conditions for the existence and uniqueness of solutions of the iterative dynamic boundary value problem of second order with mixed derivative operators. For the existence, we utilize Schauder’s fixed point theorem while for uniqueness we apply contraction mapping principle. Further, a continuous dependence of bounded solutions to the addressed problem is studied. Finally, we demonstrate the validity of our findings by constructing examples as applications to beam deflection due to thermal stress and temperature distribution along the wire.

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Data sharing not applicable to this paper as no data sets were generated or analyzed during the current study.

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Acknowledgements

The authors would like to thank the referees for their valuable suggestions and comments for the improvement of the paper. The first author, J. Alzabut, is thankful to Prince Sultan University and OSTİM Technical University for their endless support, and the second author, Mahammad Khuddush, is thankful to Dr. Lankapalli Bullayya College of Engineering for its support during the writing of this paper.

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Authors and Affiliations

  1. Department of Mathematics and Sciences, Prince Sultan University, 11586, Riyadh, Saudi Arabia

    Jehad Alzabut

  2. Department of Industrial Engineering, OSTİM Technical University, 06374, Ankara, Turkey

    Jehad Alzabut

  3. Department of Mathematics, Dr. Lankapalli Bullayya College of Engineering, Visakhapatnam, Andhra Pradesh, 530013, India

    Mahammad Khuddush

  4. Department of Mathematics, Sacred Heart College (Autonomous), Tirupattur, Tamil Nadu, 635 601, India

    A. George Maria Selvam & D. Vignesh

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  1. Jehad Alzabut
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  2. Mahammad Khuddush
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  3. A. George Maria Selvam
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  4. D. Vignesh
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The study was carried out in collaboration of all authors. All authors read and approved the final manuscript.

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Correspondence to Jehad Alzabut.

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Alzabut, J., Khuddush, M., Selvam, A.G.M. et al. Second Order Iterative Dynamic Boundary Value Problems with Mixed Derivative Operators with Applications. Qual. Theory Dyn. Syst. 22, 32 (2023). https://doi.org/10.1007/s12346-022-00736-1

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  • DOI: https://doi.org/10.1007/s12346-022-00736-1

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