Local and blowing-up solutions for a space-time fractional evolution system with nonlinearities of exponential growth

Ahmed Alsaedi, Bashir Ahmad, Mokhtar Kirane, Belgacem Rebiai

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

Local and blowing-up solutions for the Cauchy problem for a system of space and time fractional evolution equations with time-nonlocal nonlinearities of exponential growth are considered. The existence and uniqueness of the local mild solution is assured by the Banach fixed point principle. Then, we establish a blow-up result by Pokhozhaev capacity method. Finally, under some suitable conditions, an estimate of the life span of blowing-up solutions is established.

Original languageBritish English
Pages (from-to)4378-4393
Number of pages16
JournalMathematical Methods in the Applied Sciences
Volume42
Issue number12
DOIs
StatePublished - Aug 2019

Keywords

  • blow-up
  • fractional integrals and derivatives
  • life span
  • local existence
  • nonlinear fractional evolution equations

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