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35-XX Partial differential equations
35Sxx Pseudodifferential operators and other generalizations of partial differential operators
35S15 Boundary value problems for pseudodifferential operators

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Wavelet approximation methods for pseudodifferential equations: I. Stability and convergence.

W. Dahmen, S. Prössdorf, R. Schneider (1994)

Mathematische Zeitschrift

Well-Posedness of the Cauchy Problem for Inhomogeneous Time-Fractional Pseudo-Differential Equations

Saydamatov, Erkin (2006)

Fractional Calculus and Applied Analysis

Mathematics Subject Classification: 26A33, 45K05, 35A05, 35S10, 35S15, 33E12In the present paper the Cauchy problem for partial inhomogeneous pseudo-differential equations of fractional order is analyzed. The solvability theorem for the Cauchy problem in the space ΨG,2(R^n) of functions in L2(R^n) whose Fourier transforms are compactly supported in a domain G ⊆ R^n is proved. The representation of the solution in terms of pseudo-differential operators is given. The solvability theorem in the Sobolev...

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