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Fractional Resolvents and Fractional Evolution Equations

open access: yesApplied Mathematics Letters, 2012
The authors generalize the notion of strongly continuous semigroups to fractional differential equations and define the fractional resolvent. After establishing a few properties of this resolvent, the authors apply the results to a fractional-order abstract evolution equation.
Jigen Peng, Kexue Li
exaly   +4 more sources
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Liouville Equation and the Resolvent Formalism

Journal of Mathematical Physics, 1960
With the use of the Prigogine and Balescu representation for the description of relaxation starting from the Liouville equation, we apply Van Hove's resolvent formalism to obtain higher-order contributions for classical weakly coupled homogeneous gases. These results confirm Van Hove's observation that, for appropriate representations, persistent (long
Teitler, S., Wallis, R. F.
openaire   +2 more sources

Resolvent approach for the nonstationary Schrodinger equation

Inverse Problems, 1992
Summary: The spectral transform for the non-stationary Schrödinger equation is considered. The resolvent operator of the Schrödinger equation is introduced and the Fourier transform of its kernel (called the resolvent function) is studied. It is shown that it can be used to construct a generalized version of the theory of the spectral transform which ...
BOITI, Marco   +3 more
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THE RESOLVENTS OF AN EQUATION OF THE SEVENTH DEGREE

The Quarterly Journal of Mathematics, 1931
Dem Verf. gelingt es nach den klassischen Methoden der Galoisschen Theorie, zu einer in einem Rationalitätsbereich irreduziblen Gleichung 7. Grades die Galoissche Resolvente aufzustellen. Man bestimmt zunächst die transitiven Permutationsgruppen des Grades sieben (es gibt deren sieben mit den Ordnungen 5040, 2520, 168, 42, 21, 14, 7, von denen die vier
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