Globally unsolvability of fractional evolution equations with exponential nonlinearity

Achouak Bekkai (1)

1 Université Larbi Tébessi [Tebessa]

In this paper the Cauchy problem for a time-space fractional evolution equation and a system with a time nonlocal nonlinearity of exponential growth are considered. The results on existence and uniqueness of local mild solution and nonexistence of global weak solution are presented, and under some suitable conditions, an estimate of the life span of blowing-up solutions is established.

Mots clés: blow-up; fractional integrals and derivatives; life span; local existence; nonlinear fractional evolution equations

Domaines: Mathématiques [math]

Achouak Bekkai. Globally unsolvability of fractional evolution equations with exponential nonlinearity. CARI 2022, Oct 2022, Tunis, Tunisia. ⟨hal-03752999⟩