### Abstract

Let q > 1. The paper considers a linear q-difference-differential equation: it is a q-difference equation in the time variable t, and a partial differential equation in the space variable z. Under suitable conditions and by using q-Borel and q-Laplace transforms (introduced by J.-P. Ramis and C. Zhang), the authors show that if it has a formal power series solution X(t; z ) one can construct an actual holomorphic solution which admits X(t; z ) as a q-Gevrey asymptotic expansion of order 1.

Original language | English |
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Pages (from-to) | 713-738 |

Number of pages | 26 |

Journal | Opuscula Mathematica |

Volume | 35 |

Issue number | 5 |

DOIs | |

Publication status | Published - 2015 Jan 1 |

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### Keywords

- Formal power series solutions
- Q-Gevrey asymptotic expansions
- Q-Laplace transform
- Q-difference-differential equations
- Summability

### ASJC Scopus subject areas

- Mathematics(all)