Symmetry analysis of initial and boundary value problems for fractional differential equations in Caputo sense
Abstract
In this work, we study Lie symmetry analysis of initial and boundary value problems (IBVPs) for partial differential equations (PDE) with Caputo fractional derivative. According to Bluman's definition and theorem for the symmetry analysis of the PDE system, we determine the symmetries of the PDE with Caputo fractional derivative in general form and prove theorem for the above equation. We investigate the symmetry analysis of IBVP for a fractional diffusion and thirdorder fractional partial differential equation (FPDE). And as a result of applying the method, we get several solutions.
 Publication:

Chaos Solitons and Fractals
 Pub Date:
 May 2020
 DOI:
 10.1016/j.chaos.2020.109684
 arXiv:
 arXiv:1903.07946
 Bibcode:
 2020CSF...13409684I
 Keywords:

 Lie group method;
 Fractional differential equation;
 Boundary value problem;
 Mathematics  Analysis of PDEs;
 Mathematical Physics
 EPrint:
 doi:10.1016/j.chaos.2020.109684