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 EquationsCauchy ProblemCaputo Fractional DerivativeMittag-Leffler FunctionInhomogeneous EquationTime-Fractional Equation26A3345K0535A0535S1035S1533E12 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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