Abstract
We study the nonexistence of global solutions for new classes of nonlinear fractional differential inequalities. Namely, sufficient conditions are provided so that the considered problems admit no global solutions. The proofs of our results are based on the test function method and some integral estimates.
Highlights
We first consider the problem 8 >< C D10+αuðtÞ + D10+βuðtÞ ≥ Dγ0 uðt Þp, t > >: uð0Þ, u ′
A function u ∈ AC2ð1⁄20,∞ÞÞ is said to be a global solution to problem (1), if u satisfies
A function u ∈ AC2ð1⁄20,∞ÞÞ is said to be a global solution to problem (2), if u satisfies
Summary
Þ, ð1Þ where p > 1, α, β, γ ∈ ð0, 1Þ, CDκ0, κ ∈ f1 + α, 1 + β, γg is the Caputo fractional derivative of order κ, u0 ∈ R, and u1 ≥ 0. If pð1 − βÞ − 1 < γ < p − 1, ð5Þ problem (4) does not admit nontrivial global solution. For the issue of nonexistence of global solutions for fractional in time evolution equations, we refer to [6, 23,24,25] and the references therein. A function u ∈ AC2ð1⁄20,∞ÞÞ is said to be a global solution to problem (2), if u satisfies. (i) If σ ≥ 0, for all p > 1, problem (2) admits no global solution (ii) Let −1 < σ < 0.
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