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

Saydamatov, 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 -