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Study of three-point impulsive boundary value problems governed by \(\Psi \)-Caputo fractional derivative

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Abstract

In this study, we investigate the existence and uniqueness of solutions for specific type of three-point boundary value problems. These problems focus on nonlinear impulsive fractional differential equations, which pose a challenge in finding their solutions. To address this, we employ fixed point theorems of Banach and Schauder as mathematical tools to establish the existence, and uniqueness of solutions. The comparison between analytical outcomes and illustrative examples provides valuable insights into the accuracy and reliability of the derived solutions, enhancing their applicability in various fields.

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Acknowledgements

V. Govindaraj would like to thank the National Board for Higher Mathematics (NBHM), Department of AtomicEnergy, Government of India, for funding the research project (File No. 02011/18/2023 NBHM (R.P)/ R& DII/5952).

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Authors and Affiliations

  1. Department of Mathematics, National Institute of Technology Puducherry, Karaikal, 609609, India

    R. Poovarasan & V. Govindaraj

  2. Department of Mathematics, Faculty of Science, Bu-Ali Sina University, Hamadan, Iran

    Mohammad Esmael Samei

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Poovarasan, R., Samei, M.E. & Govindaraj, V. Study of three-point impulsive boundary value problems governed by \(\Psi \)-Caputo fractional derivative. J. Appl. Math. Comput. 70, 3947–3983 (2024). https://doi.org/10.1007/s12190-024-02122-3

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