Azman, IbtehalJleli, MohamedKirane, MokhtarSamet, Bessem2022-08-192022-08-192017-11-08Azman, I., Jleli, M., Kirane, M., & Samet, B. (2017). Nonexistence of global solutions for fractional temporal Schrödinger equations and systems. <i>Electronic Journal of Differential Equations, 2017</i>(276), pp. 1-17.1072-6691https://hdl.handle.net/10877/16077We, first, consider the nonlinear Schrödinger equation iαC0 Dαtu + ∆u = λ|u|p + μα(x) ‧ ∇|u|q, t > 0, x ∈ ℝN, where 0 < α < 1, iα is the principal value of iα, C0 Dαt is the Caputo fractional derivative of order α, λ ∈ ℂ\ {0}, μ ∈ ℂ, p > q > 1, u(t, x) is a complex-valued function, and α : ℝN → ℝN is a given vector function. We provide sufficient conditions for the nonexistence of global weak solution under suitable initial data. Next, we extend our study to the system of nonlinear coupled equations iαC0 Dαtu + ∆u = λ|v|p> + μα(x) ‧ ∇|v|q, t > 0, x ∈ ℝN, iβC0 Dβtv + ∆v = λ|u|k + μb(x) ‧ ∇|u|σ, t > 0, x ∈ ℝN, where 0 < β ≤ α < 1, λ ∈ ℂ\{0}, μ ∈ ℂ, p > q > 1, k > σ > 1, and α, b : ℝN → ℝN are two given vector functions. Our approach is based on the test function method.Text17 pages1 file (.pdf)enAttribution 4.0 InternationalFractional temporal Schrödinger equationNonexistenceGlobal weak solutionArticle