Displaying similar documents to “Fractional Derivatives and Fractional Powers as Tools in Understanding Wentzell Boundary Value Problems for Pseudo-Differential Operators Generating Markov Processes”

Linear Fractional PDE, Uniqueness of Global Solutions

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

Fractional Calculus and Applied Analysis

Similarity:

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.

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

Saydamatov, Erkin (2006)

Fractional Calculus and Applied Analysis

Similarity:

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...

A Fractional Analog of the Duhamel Principle

Umarov, Sabir, Saydamatov, Erkin (2006)

Fractional Calculus and Applied Analysis

Similarity:

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. ...

On the Operational Solution of a System of Fractional Differential Equations

Takači, Dj., Takači, A. (2010)

Fractional Calculus and Applied Analysis

Similarity:

MSC 2010: 26A33, 44A45, 44A40, 65J10 We consider a linear system of differential equations with fractional derivatives, and its corresponding system in the field of Mikusiński operators, written in a matrix form, by using the connection between the fractional and the Mikusiński calculus. The exact and the approximate operational solution of the corresponding matrix equations, with operator entries are determined, and their characters are analyzed. By using the packages...

Fractional Calculus of the Generalized Wright Function

Kilbas, Anatoly (2005)

Fractional Calculus and Applied Analysis

Similarity:

Mathematics Subject Classification: 26A33, 33C20. The paper is devoted to the study of the fractional calculus of the generalized Wright function pΨq(z) defined for z ∈ C, complex ai, bj ∈ C and real αi, βj ∈ R (i = 1, 2, · · · p; j = 1, 2, · · · , q) by the series pΨq (z) It is proved that the Riemann-Liouville fractional integrals and derivative of the Wright function are also the Wright functions but of greater order. Special cases are considered. * The present...