2023/05/01 by Xiaoyu Cheng, Lizhen Wang, Cheng, Xiaoyu +1
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Analysis of PDEs (math.AP) #FOS: Mathematics #Fractional Differential Equations Solutions #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.2305.00778
openalex publication_date 2023/05/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, the relationships between Lie symmetry groups and fundamental solutions for a class of conformable time fractional partial differential equations (PDEs) with variable coefficients are investigated. Specifically, the group-invariant solutions to the considered equations are constructed applying symmetry group method and the corresponding fundamental solutions for these systems are established with the help of the above obtained group-invariant solutions and inverting Laplace transformation. In addition, the connections between fundamental solutions for two conformable time fractional systems are given by equivalence transformation. Furthermore, the conservation laws of these fractional systems are provided using new Noether theorem and obtained Lie algebras.