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

Fractional Calculus and Applied Analysis (2006)

- Volume: 9, Issue: 1, page 01-16
- ISSN: 1311-0454

## Access Full Article

top## Abstract

top## How to cite

topSaydamatov, Erkin. "Well-Posedness of the Cauchy Problem for Inhomogeneous Time-Fractional Pseudo-Differential Equations." Fractional Calculus and Applied Analysis 9.1 (2006): 01-16. <http://eudml.org/doc/11304>.

@article{Saydamatov2006,

abstract = {Mathematics Subject Classification: 26A33, 45K05, 35A05, 35S10, 35S15, 33E12In 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.},

author = {Saydamatov, Erkin},

journal = {Fractional Calculus and Applied Analysis},

keywords = {26A33; 45K05; 35A05; 35S10; 35S15; 33E12},

language = {eng},

number = {1},

pages = {01-16},

publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},

title = {Well-Posedness of the Cauchy Problem for Inhomogeneous Time-Fractional Pseudo-Differential Equations},

url = {http://eudml.org/doc/11304},

volume = {9},

year = {2006},

}

TY - JOUR

AU - Saydamatov, Erkin

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

JO - Fractional Calculus and Applied Analysis

PY - 2006

PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences

VL - 9

IS - 1

SP - 01

EP - 16

AB - Mathematics Subject Classification: 26A33, 45K05, 35A05, 35S10, 35S15, 33E12In 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.

LA - eng

KW - 26A33; 45K05; 35A05; 35S10; 35S15; 33E12

UR - http://eudml.org/doc/11304

ER -

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.