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This is a Quantitative Study study.

October 20, 2025Open Access

Local/global well-posedness analysis of time-space fractional Schrödinger equation on R^d

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Investigation demonstrates well-posedness of time-space fractional Schrödinger equations, implying significant nonlocal effects in analysis.

Establishing global/local well-posedness relies on the Gagliardo-Nirenberg inequality in a specific function space, important for advanced mathematical studies.
Key methods include the asymptotic behavior of Mittag-Leffler functions and Hörmander multiplier theory, both essential for addressing nonlocal effects.
Sobolev estimates for the solution operator are derived, enhancing understanding of fractional Schrödinger equations in nonlinear dynamics.
Results provide critical insights complementary to previous work while employing distinct analytical methods.

Yang et al. (2025) studied this question.

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Investigation demonstrates well-posedness of time-space fractional Schrödinger equations, implying significant nonlocal effects in analysis.