Electron. J. Diff. Equ., Vol. 2016 (2016), No. 20, pp. 1-14.

Nonexistence of solutions to Cauchy problems for fractional time semi-linear pseudo-hyperbolic systems

Salem Abdelmalek, Maha Bajneed, Khaled Sioud

Abstract:
We study Cauchy problems time fractional semi-linear pseudo-hyperbolic equations and systems. Using the method of nonlinear capacity, we show that there are no solutions for certain nonlinearities and initial data. Our work complements the work by Aliev and col. [1,6,7].

Submitted June 25, 2015. Published January 12, 2016.
Math Subject Classifications: 80A23, 65N21, 26A33, 45J05, 34K37, 42A16.
Key Words: Semi-linear pseudo-hyperbolic equation; non-existence of solutions; non-linear capacity method.

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  Salem Abdelmalek
Department of Mathematics
College of Sciences at Yanbu
Taibah University, Saudi Arabia
email: sallllm@gmail.com
  Maha Bajneed
Department of Mathematics
Faculty of Sciences at Yanbu
Taibah University, Saudi Arabia
email: m_bajneed@hotmail.com
Khaled Sioud
Department of Mathematics
Faculty of Sciences at Yanbu
Taibah University, Saudi Arabia
email: sioudkha@aol.com

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