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Analytical treatment of regularized Prabhakar fractional differential equations by invariant subspaces

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Abstract

This work is devoted to the time-fractional differential equations with the regularized Prabhakar derivative and their analytical solutions. We generalize the invariant subspace method to find the exact solutions of such equations. Then, we apply this method to obtain the exact solutions of different time-fractional nonlinear differential equations including the regularized Prabhakar derivative.

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Notes

  1. Here, \(\star \) stands for the convolution.

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Authors and Affiliations

  1. Institute for Advanced Study Honoring Chen Jian Gong, Hangzhou Normal University, Hangzhou, 311121, People’s Republic of China

    Y.-M. Chu

  2. Department of Mathematics, Huzhou University, Huzhou, 313000, People’s Republic of China

    Y.-M. Chu

  3. Department of Mathematics, Science Faculty, Firat University, 23119, Elazig, Turkey

    Mustafa Inc

  4. Department of Medical Research, China Medical University, Taichung, Taiwan

    Mustafa Inc

  5. Department of Mathematics, Basic Science Faculty, University of Bonab, P.O. Box 55513-95133, Bonab, Iran

    M. S. Hashemi

  6. Department of Applied Mathematics, Faculty of Mathematical Sciences, Shahrekord University, Shahrekord, Iran

    S. Eshaghi

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  1. Y.-M. Chu
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  2. Mustafa Inc
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  3. M. S. Hashemi
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  4. S. Eshaghi
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Correspondence to Mustafa Inc.

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Communicated by Roberto Garrappa.

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Chu, YM., Inc, M., Hashemi, M.S. et al. Analytical treatment of regularized Prabhakar fractional differential equations by invariant subspaces. Comp. Appl. Math. 41, 271 (2022). https://doi.org/10.1007/s40314-022-01977-1

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  • DOI: https://doi.org/10.1007/s40314-022-01977-1

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