SOLUTION OF FRACTIONAL DIFFUSION-WAVE EQUATIONS IN A FRACTIONAL VISCOELASTIC MEDIA
To provide a mechanical explanation of deformation and ow of viscoelastic material in Rheology, a fractional viscoelastic model was developed through the application of fractional calculus. A fractional diusion-wave equations in a fractional viscoelastic media can be constructed by using equati...
Saved in:
| Main Author: | |
|---|---|
| Format: | Theses |
| Language: | Indonesia |
| Online Access: | https://digilib.itb.ac.id/gdl/view/65442 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Institution: | Institut Teknologi Bandung |
| Language: | Indonesia |
| Summary: | To provide a mechanical explanation of deformation and
ow of viscoelastic
material in Rheology, a fractional viscoelastic model was developed through
the application of fractional calculus. A fractional diusion-wave equations in
a fractional viscoelastic media can be constructed by using equations of mo-
tion and kinematic equations of viscoelastic material in fractional order. This
thesis concerns the fractional diusion-wave equations in the fractional visco-
elastic media for semi-innite regions that satises signalling boundary value
problems. Fractional derivatives was used in Caputo sense. The analytical
solution of the fractional diusion-wave equations in the fractional viscoelastic
media was solved by means of Laplace transform techniques in the term of
Wright function for simple form solutions. For certain parameters, the eect
will start from a certain amplitude when t x
c and when t < x
c no movement
occurs, c is wave velocity and it was assumed to be nite. For general para-
meters, Numerical Inverse Laplace Transforms (NILT) was used to determine
the solution. |
|---|