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New generalized integral transform on Hilfer–Prabhakar fractional derivatives and its applications

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Abstract

In this paper, we obtain the new generalized integral transform of the Prabhakar integral, Prabhakar derivative, and Hilfer–Prabhakar fractional derivatives. Using these results, we obtained several existing results for different integral transforms by varying the unknown functions \(\psi (s)\) and \(\phi (s)\). Next, using Hilfer–Prabhakar derivatives, a three-parameter Mittage-Leffler function (MLF), a contemporary integral transform, and a Fourier transform, we evaluate the solutions to a few fractional differential equations of the Cauchy-type.

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Acknowledgements

The authors are very thankful to the Department of Mathematics, School of Sciences, Maulana Azad National Urdu University for Providing Research facilities and financial support for the Research Scholars. The authors wish to express their sincere thanks to anonymous referees.

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  1. Mohd Khalid and Subhash Alha have contributed equally to this work.

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  1. Department of Mathematics, Maulana Azad National Urdu University, Gachibowli, Hyderabad, 500032, India

    Mohd Khalid & Subhash Alha

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  1. Mohd Khalid
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  2. Subhash Alha
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Khalid, M., Alha, S. New generalized integral transform on Hilfer–Prabhakar fractional derivatives and its applications. Int. J. Dynam. Control 12, 24–31 (2024). https://doi.org/10.1007/s40435-023-01235-0

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  • DOI: https://doi.org/10.1007/s40435-023-01235-0

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