On Fractional Helmholtz Equations

Samuel, M., and Thomas, Anitha. "On Fractional Helmholtz Equations." Fractional Calculus and Applied Analysis 13.3 (2010): 295-308. <http://eudml.org/doc/219641>.

@article{Samuel2010,
abstract = {MSC 2010: 26A33, 33E12, 33C60, 35R11In this paper we derive an analytic solution for the fractional Helmholtz equation in terms of the Mittag-Leffler function. The solutions to the fractional Poisson and the Laplace equations of the same kind are obtained, again represented by means of the Mittag-Leffler function. In all three cases the solutions are represented also in terms of Fox's H-function.},
author = {Samuel, M., Thomas, Anitha},
journal = {Fractional Calculus and Applied Analysis},
keywords = {Fractional Helmholtz Equation; Caputo Fractional Derivative; Weyl Fractional Derivative; Mittag-Leffler Function; Fox's H-function; fractional Helmholtz equation; Caputo fractional derivative; Weyl fractional derivative; Mittag-Leffler function; Fox’s -function},
language = {eng},
number = {3},
pages = {295-308},
publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},
title = {On Fractional Helmholtz Equations},
url = {http://eudml.org/doc/219641},
volume = {13},
year = {2010},
}

TY - JOUR
AU - Samuel, M.
AU - Thomas, Anitha
TI - On Fractional Helmholtz Equations
JO - Fractional Calculus and Applied Analysis
PY - 2010
PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences
VL - 13
IS - 3
SP - 295
EP - 308
AB - MSC 2010: 26A33, 33E12, 33C60, 35R11In this paper we derive an analytic solution for the fractional Helmholtz equation in terms of the Mittag-Leffler function. The solutions to the fractional Poisson and the Laplace equations of the same kind are obtained, again represented by means of the Mittag-Leffler function. In all three cases the solutions are represented also in terms of Fox's H-function.
LA - eng
KW - Fractional Helmholtz Equation; Caputo Fractional Derivative; Weyl Fractional Derivative; Mittag-Leffler Function; Fox's H-function; fractional Helmholtz equation; Caputo fractional derivative; Weyl fractional derivative; Mittag-Leffler function; Fox’s -function
UR - http://eudml.org/doc/219641
ER -