**Absence of Global Solutions for a Fractional in Time and Space Shallow-Water System**

**Mohamed Jleli 1, Mokhtar Kirane 2,3,\* and Bessem Samet <sup>1</sup>**


Received: 12 October 2019; Accepted: 15 November 2019; Published: 18 November 2019

**Abstract:** An initial boundary value problem for a fractional in time and space shallow-water system involving *ψ*-Caputo fractional derivatives of different orders is considered. Using the test function method, sufficient criteria for the absence of global in time solutions of the system are obtained.

**Keywords:** global solutions; fractional in time and space shallow-water system; *ψ*-Caputo fractional derivative

**MSC:** 35B44; 26A33
