Lorenzo-Hartley G-function (lhg_fun)

LHG(Lorenzo, Hartley G- Function) -

A Generalized Function for the Fractional Calculus

Reference:Generalized Functions for the Fractional Calculus Carl F. Lorenzo, Glenn Research Center, Cleveland, Ohio
Tom T. Hartley, The University of Akron, Akron, Ohio NASA/TP—1999-209424/REV1

Prepared by S.C. Pandey, 22/08/2013

Based on the codes given in Dingyu Xue, YangQuan Chen and Derek Atherton.
Linear Feedback Control Analysis and Design with Matlab. SIAM Press, 2007,
ISBN: 978-0-898716-38-2. (348 pages)

LHG function is denoted as
'G_{\nu,\mu,\delta}(a,x)'
a: \nu \in C, and \re{\nu) >0
b: \mu \in C, and \re{\mu) >0
c: \delta \in C, and \re{\delta) >0
d: Constant
x: The variable
eps0: specified accuracy

LHG_FUN can also be put in to the function involving GML_FUN Prepared by
YangQuan Chen. 07/23/2008 based on
'A. A. KILBAS, M. SAIGOb, and R. K. SAXENA, Generalized Mittag-Leffler function and generalized fractional calculus operators', Integral Transforms and Special Functions, vol. 15, No. 1, 2004, pp. 3149.

It can be used to solve various problems related to fractional calculus like we are using it to solve FKE in 'On the new computable solution of the generalized fractional kinetic equations involving the generalized functionfor the fractional calculus and related functions'Astrophys Space Sci (2008) 317: 213–219.