Displaying similar documents to “Well-Posedness of the Cauchy Problem for Inhomogeneous Time-Fractional Pseudo-Differential Equations”

A Fractional Analog of the Duhamel Principle

Umarov, Sabir, Saydamatov, Erkin (2006)

Fractional Calculus and Applied Analysis

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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. ...

Fractional Derivatives and Fractional Powers as Tools in Understanding Wentzell Boundary Value Problems for Pseudo-Differential Operators Generating Markov Processes

Jacob, N., Knopova, V. (2005)

Fractional Calculus and Applied Analysis

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Mathematics Subject Classification: 26A33, 31C25, 35S99, 47D07. Wentzell boundary value problem for pseudo-differential operators generating Markov processes but not satisfying the transmission condition are not well understood. Studying fractional derivatives and fractional powers of such operators gives some insights in this problem. Since an L^p – theory for such operators will provide a helpful tool we investigate the L^p –domains of certain model operators. ...

Linear Fractional PDE, Uniqueness of Global Solutions

Schäfer, Ingo, Kempfle, Siegmar, Nolte, Bodo (2005)

Fractional Calculus and Applied Analysis

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Mathematics Subject Classification: 26A33, 47A60, 30C15. In this paper we treat the question of existence and uniqueness of solutions of linear fractional partial differential equations. Along examples we show that, due to the global definition of fractional derivatives, uniqueness is only sure in case of global initial conditions.

Pseudo-Differential Operators in a Wave Diffraction Problem with Impedance Conditions

Castro, L.P., Kapanadze, D. (2008)

Fractional Calculus and Applied Analysis

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Mathematics Subject Classification: 35J05, 35J25, 35C15, 47H50, 47G30 We consider an impedance boundary-value problem for the Helmholtz equation which models a wave diffraction problem with imperfect conductivity on a strip. Pseudo-differential operators are used to deal with this wave diffraction problem. Therefore, single and double layer potentials allow a reformulation of the problem into a system of integral equations. By using operator theoretical methods, the well-posedness...

Cauchy-Type Problem for Diffusion-Wave Equation with the Riemann-Liouville Partial Derivative

Kilbas, Anatoly, Trujillo, Juan, Voroshilov, Aleksandr (2005)

Fractional Calculus and Applied Analysis

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2000 Mathematics Subject Classification: 35A15, 44A15, 26A33 The paper is devoted to the study of the Cauchy-type problem for the differential equation [...] involving the Riemann-Liouville partial fractional derivative of order α > 0 [...] and the Laplace operator.

LP → LQ - Estimates for the Fractional Acoustic Potentials and some Related Operators

Karapetyants, Alexey, Karasev, Denis, Nogin, Vladimir (2005)

Fractional Calculus and Applied Analysis

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Mathematics Subject Classification: 47B38, 31B10, 42B20, 42B15. We obtain the Lp → Lq - estimates for the fractional acoustic potentials in R^n, which are known to be negative powers of the Helmholtz operator, and some related operators. Some applications of these estimates are also given. * This paper has been supported by Russian Fond of Fundamental Investigations under Grant No. 40–01–008632 a.