Geodesic
New trends on fractional integral and differential equations
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Труды геометрического семинара, Tome 147 (2005) no. 1, pp. 72-106

Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

One- and multi-dimensional integral equations and ordinary and partial differential equations with fractional integrals and derivatives by Riemann–Liouville, Liouville, Caputo, Hadamard and Riesz are considered. The method based on the reduction of the Cauchy-type and Cauchy problems for the one-dimensional nonlinear fractional differential equations to Volterra integral equations is discussed. A unified approach is presented to solve in close form of some classes of one- and multi-dimensional linear integral equations and linear ordinary and partial differential equations of fractional order. This approach is based on compositional relations, operational calculus and integral transforms by Laplace, Fourier and Mellin. Problems and new trends of research are discussed. 
@article{UZKU_2005_147_1_a8,
     author = {A. A. Kilbas},
     title = {New trends on fractional integral and differential equations},
     journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
     pages = {72--106},
     publisher = {mathdoc},
     volume = {147},
     number = {1},
     year = {2005},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/UZKU_2005_147_1_a8/}
}
TY  - JOUR
AU  - A. A. Kilbas
TI  - New trends on fractional integral and differential equations
JO  - Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki
PY  - 2005
SP  - 72
EP  - 106
VL  - 147
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/UZKU_2005_147_1_a8/
LA  - en
ID  - UZKU_2005_147_1_a8
ER  - 
%0 Journal Article
%A A. A. Kilbas
%T New trends on fractional integral and differential equations
%J Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki
%D 2005
%P 72-106
%V 147
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/UZKU_2005_147_1_a8/
%G en
%F UZKU_2005_147_1_a8
A. A. Kilbas. New trends on fractional integral and differential equations. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Труды геометрического семинара, Tome 147 (2005) no. 1, pp. 72-106. http://geodesic.mathdoc.fr/item/UZKU_2005_147_1_a8/