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Evolution equations with fractional Gross Laplacian and Caputo time fractional derivative

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Abstract

In this paper, we consider the evolution equations with fractional Gross Laplacian and generalized Caputo time fractional deravitive in infinite dimensional space of entire functions with growth condition. The convolution between a generalized function related to the Mittag–Leffler function and the initial condition has been given to demonstrate the explicit solutions. Moreover, we prove that the fundamental solution is related to the inverse stable subordinators and the symmetric \(\alpha \)-stable distribution.

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Acknowledgements

The authors would like to express their sincere thanks to the anonymous reviewers for their valuable suggestions and corrections for improving the quality of the paper.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Sciences, University of Tunis El Manar, 1060, Tunis, Tunisia

    Abdeljabbar Ghanmi & Samah Horrigue

  2. Department of Mathematics, Faculty of Sciences and Arts Khulais, University of Jeddah, Jeddah, Kingdom of Saudi Arabia

    Samah Horrigue

Authors
  1. Abdeljabbar Ghanmi
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  2. Samah Horrigue
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Correspondence to Abdeljabbar Ghanmi.

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Communicating Editor: E K Narayanan

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Ghanmi, A., Horrigue, S. Evolution equations with fractional Gross Laplacian and Caputo time fractional derivative. Proc Math Sci 129, 80 (2019). https://doi.org/10.1007/s12044-019-0507-7

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  • DOI: https://doi.org/10.1007/s12044-019-0507-7

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