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Please use this identifier to cite or link to this item: http://hdl.handle.net/10525/1268

Title: Well-Posedness of the Cauchy Problem for Inhomogeneous Time-Fractional Pseudo-Differential Equations
Authors: Saydamatov, Erkin
Keywords: Pseudo-Differential Equations
Cauchy Problem
Caputo Fractional Derivative
Mittag-Leffler Function
Inhomogeneous Equation
Time-Fractional Equation
26A33
45K05
35A05
35S10
35S15
33E12
Issue Date: 2006
Publisher: Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Citation: Fractional Calculus and Applied Analysis, Vol. 9, No 1, (2006), 01p-16p
Abstract: In 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 spaces H^s,2(R^n), s ∈ R^1 is also established.
Description: Mathematics Subject Classification: 26A33, 45K05, 35A05, 35S10, 35S15, 33E12
URI: http://hdl.handle.net/10525/1268
ISSN: 1311-0454
Appears in Collections:2006

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