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Global optimization of a nonlinear system of differential equations involving \(\psi \)-Hilfer fractional derivatives of complex order

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Abstract

In this paper, a class of cyclic (noncyclic) operators of condensing nature are defined on Banach spaces via a pair of shifting distance functions. The best proximity point (pair) results are manifested using the concept of measure of noncompactness (MNC) for the said operators. The obtained best proximity point result is used to demonstrate existence of optimum solutions of a system of differential equations involving \(\psi \)-Hilfer fractional derivatives of complex order.

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Acknowledgements

The authors thank the Editor and anonymous referees for their helpful comments that improved the quality of the manuscript.

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Authors and Affiliations

  1. Department of Mathematics, School of Applied Sciences, VIT-AP University, Amravati, Andhra Pradesh, 522034, India

    Pradip Ramesh Patle

  2. Department of Mathematics, Ayatollah Boroujerdi University, Boroujerd, Iran

    Moosa Gabeleh

  3. Department of Mathematics, Faculty of Sciences and Mathematics, Višegradska 33, Niš, 18000, Serbia

    Vladimir Rakočević

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  1. Pradip Ramesh Patle
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  2. Moosa Gabeleh
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  3. Vladimir Rakočević
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Correspondence to Vladimir Rakočević.

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Patle, P.R., Gabeleh, M. & Rakočević, V. Global optimization of a nonlinear system of differential equations involving \(\psi \)-Hilfer fractional derivatives of complex order. Fract Calc Appl Anal (2024). https://doi.org/10.1007/s13540-024-00260-w

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  • DOI: https://doi.org/10.1007/s13540-024-00260-w

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