Evolution equations with fractional Gross Laplacian and Caputo time fractional derivative

  • Abdeljabbar GhanmiEmail author
  • Samah Horrigue


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.


Generalized fractional Gross Laplacian Young function infinite dimensional entire functions with growth condition Caputo derivative symmetric \(\alpha \)-stable distribution 

2000 Mathematics Subject Classification

60H15 46F25 26A33 60H05 46G20 



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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Copyright information

© Indian Academy of Sciences 2019

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of SciencesUniversity of Tunis El ManarTunisTunisia
  2. 2.Department of Mathematics, Faculty of Sciences and Arts KhulaisUniversity of JeddahJeddahKingdom of Saudi Arabia

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