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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, 33E12 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...

A Fractional Analog of the Duhamel Principle

Umarov, Sabir;  Saydamatov, Erkin — 2006

Fractional Calculus and Applied Analysis

Mathematics Subject Classification: 35CXX, 26A33, 35S10 The well known Duhamel principle allows to reduce the Cauchy problem for linear inhomogeneous partial differential equations to the Cauchy problem for corresponding homogeneous equations. In the paper one of the possible generalizations of the classical Duhamel principle to the time-fractional pseudo-differential equations is established. * This work partially supported by NIH grant P20 GMO67594.

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