@Carl Love 

Thanks.  I appreciate your looking into the possibilities.  I will look

at the works based on direct Fortran solutions to see if there are

any clues--

@Carl Love 

Yes, physically beta is usually less than one--say, 0.6 to 0.85 or so (this produces a very expanded-{compared to simple exponential}- relaxation time range and generates the peculiar kinetics of glass relaxation.  Sometimes beta is

referred to as a "fractal time dimension".

other typical parameter values would be a=3, b=20,000, y1=10, t=5000.  Many thanks--John

@Carl Love 

Wonderful!-thank you very much Carl--This will save me much time and probably help me avoid many mistakes

along the way (FYI-the equation in question describes the way in which a molten glassy material slowly densifies after it has been cooled rapidly to a solid.)

Many thanks--John

@Carl Love 

Thank you very much Carl.  I am presently trying to familiarize myself with ODE and I hope it

will also prove to be applicable to several other related problems--Your assistance is much appreciated--Best--John

@Preben Alsholm 

Sir--Thank you very much.  Your comments regarding tm make sense.  My times t (or z) are only positive,

so the fix you suggest is fine.  Many thanks indeed--Regards--John