SOLUTION OF FRACTIONAL DIFFUSION-WAVE EQUATIONS IN A FRACTIONAL VISCOELASTIC MEDIA - Novita Yasa, Ray
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.