In this paper, we consider the time‐fractional order Schrödinger equation that is a fundamental equation in fractional quantum mechanics. By using the spectral theorem, we prove Duhamel''s formula and give some properties of solution operators, which can be used to study the local existence ...
the Duhamel formula (6). Criterion (9) is a generalised compatibility condition on the data (f,uT); such conditions have long been known in the theory of parabolic problems, cf. Remark 7. The presence of e−(T−t)A and the integral over [0,T] makes (9) non-local in both ...
By using the spectral theorem, we prove Duhamel''s formula and give some properties of solution operators, which can be used to study the local existence and the global existence of time‐fractional Schrödinger equations on a Hilbert space.关键词: Caputo fractional derivative Duhamel''s formula...
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In this paper, we consider the time-fractional order Schrodinger equation that is a fundamental equation in fractional quantum mechanics. By using the spectral theorem, we prove Duhamel's formula and give some properties of solution operators, which can be used to study the local existence and ...
No Abstract available for this article.doi:10.1007/BF01200374Rhoda J. HughesBirkhäuser-VerlagIntegral Equations and Operator Theory
The solution of heat equation inside oscillating gas bubble with moving boundary was obtained by Fourier's method. The integral formula for interface heat flux, containing theta-function in the integrand was derived. The kernel of the integral is represented by a series of exponential functions, ...
The paper considers the initial boundary value problem for the wave equation for the case of three spatial variables. The definition of a generalized solution has been introduced and the theorem of unique existence has been proved. A new formula was proposed, being an analog of the well-known ...
The Duhamel product of functions f and g is defined by the formula (f * g)(x) = d/(dx) ∫_0~x f(x-t)g(t)dt. In the present paper, the Duhamel product is used in the study of spectral multiplicity for direct sums of operators and in the description of cyclic vectors of the...
The Duhamel product of functions f and g is defined by the formula $$(f \\circledast g)(x) = \\frac{d}{{dx}}\\int\\limits_0^x {f(x - t)g(t)dt.}$$ . In the present paper, the Duhamel product is used in the study of spectral multiplicity for direct sums of operators ...